18 medium SAT Linear equations · one variable questions
Medium is where most scores are actually won and lost. These questions are not tricky for the sake of it, but every one of them has a wrong answer built to catch a specific shortcut.
Every question below is a real item from the SAT Climb bank, tagged medium by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
What is the value of x in the equation 8(x−4)=6(x+2)?
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Why C is right
Expanding both sides gives 8x−32=6x+12. Subtracting 6x from both sides yields 2x−32=12. Adding 32 to both sides gives 2x=44, so x=22.
Why the others are wrong
AThis results from a sign error when moving terms or combining constants across the equation.
BThis results from swapping operations or incorrectly handling the distributive property.
DThis results from not dividing by the correct coefficient after isolating the variable term.
Question 2Medium
The equation d=520−8t represents the distance d, in miles, remaining in a trip after t hours of driving.
According to the equation, what is the total distance of the trip, in miles?
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Why D is right
The total distance of the trip is the distance remaining when t=0, which is d=520−8(0) = 520 miles. This is the starting value before any driving has occurred.
Why the others are wrong
AThis is the rate of travel (8 miles per hour) rather than the total distance.
BThis divides 520 by 8, finding the time to complete the trip rather than the total distance.
CThis subtracts 8 from 520, incorrectly treating 8 as a fixed subtraction rather than a rate coefficient.
Question 3Medium
The equation H=2400+150m models the total number of hours H of content available on a streaming service after m months. Which of the following is the best interpretation of the number 2400 in this context?
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Why B is right
In the equation H=2400+150m, the constant term 2400 represents the value of H when m=0. This is the initial number of hours of content available at the start.
Why the others are wrong
AThis interprets 2400 as the rate of change, which is actually represented by the coefficient 150.
CThis incorrectly treats 2400 as a product of 150 and some number rather than as the initial constant value.
DThis assigns the wrong sign to 2400; the positive constant indicates the starting amount, and the equation shows content is being added, not removed.
Question 4Medium
What is the value of x in the equation 4(3x−2)=5(2x+4)?
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Why A is right
Expanding both sides gives 12x−8=10x+20. Subtracting 10x from both sides yields 2x−8=20. Adding 8 to both sides gives 2x=28, so x=14.
Why the others are wrong
BThis results from a sign error when computing -8 - 20 instead of correctly moving -8 to the right side as +8.
CThis results from incorrectly treating 20 + 8 = 28 and then dividing by 3 instead of 2.
DThis results from correctly getting 2x = 28 but then dividing 28 by 4 instead of 2.
Question 5Medium
What is the value of x in the equation 2(x−7)+3x=4(x+2)?
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Why D is right
Expanding gives 2x−14+3x=4x+8, which simplifies to 5x−14=4x+8. Subtracting 4x from both sides yields x−14=8. Adding 14 to both sides gives x=22.
Why the others are wrong
AThis results from a sign error when combining terms or moving constants across the equation.
BThis results from using an incorrect coefficient when simplifying or isolating x.
CThis results from swapping operations or prematurely dividing by a coefficient.
Question 6Medium
The equation D=180−25t models the distance D, in miles, remaining to a destination after driving for t hours. Which of the following is the best interpretation of the number 25 in this context?
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Why A is right
In the equation D=180−25t, the coefficient 25 is multiplied by t (time in hours) and represents the number of miles covered per hour. This is the speed of the car.
Why the others are wrong
BThis confuses the rate (miles per hour) with the time variable t itself.
CThis interprets 25 as the initial distance, which is actually represented by the constant 180.
DThis assigns the wrong sign interpretation; the negative sign means the remaining distance decreases, so 25 represents the rate of decrease in remaining distance, which is the same as the speed of travel.
Question 7Medium
What is the value of x in the equation 6(x−4)=4(x−1)?
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Why B is right
Expanding both sides gives 6x−24=4x−4. Subtracting 4x from both sides yields 2x−24=−4. Adding 24 to both sides gives 2x=20, so x=10.
Why the others are wrong
AThis results from incorrectly calculating the difference between constant terms during the solving process.
CThis results from a sign error when combining terms or isolating the variable.
DThis is the value of 2x, not x, resulting from failing to complete the final division step.
Question 8Medium
What is the value of x in the equation 4(x+5)=3(2x−4)?
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Why B is right
Expanding both sides gives 4x+20=6x−12. Subtracting 4x from both sides yields 20=2x−12. Adding 12 to both sides gives 32=2x, so x=16.
Why the others are wrong
AThis results from using an incorrect coefficient when dividing or combining terms.
CThis results from a sign error when moving terms or simplifying the equation.
DThis results from swapping the order of operations or incorrectly handling the distributive property.
Question 9Medium
The equation C=45+12h models the total cost C, in dollars, to rent a bicycle for h hours. Which of the following is the best interpretation of the number 45 in this context?
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Why B is right
In the equation C=45+12h, the term 45 is the constant term that is added regardless of the value of h. This represents the initial or fixed cost to rent the bicycle before counting any hours.
Why the others are wrong
AThis interprets 45 as the hourly rate, which is actually represented by the coefficient 12.
CThis incorrectly treats 45 as the result of multiplying 12 by some number of hours rather than as the constant initial cost.
DThis assigns the wrong sign to 45; the positive constant represents an added cost, not a decrease.
Question 10Medium
What is the value of x in the equation 2(3x−5)=4(x+1)?
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Why A is right
Expanding both sides gives 6x−10=4x+4. Subtracting 4x from both sides yields 2x−10=4. Adding 10 to both sides gives 2x=14, so x=7.
Why the others are wrong
BThis results from incorrectly combining coefficients or constants during the solving process.
CThis results from a sign error when moving terms or simplifying.
DThis is the value of 2x, not x, resulting from failing to complete the final division step.
Question 11Medium
What is the value of x in the equation 8(x − 4) = 6(x+2)?
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Why B is right
Expanding both sides gives 8x − 32=6x+12. Subtracting 6x from both sides yields 2x − 32 = 12. Adding 32 to both sides gives 2x=44, so x=22.
Why the others are wrong
AThis results from incorrectly manipulating the constants or coefficients during the solving process.
CThis results from an error in sign when isolating the variable or combining constants.
DThis is the value of 2x rather than x, resulting from failing to complete the final division step.
Question 12Medium
The equation L=95−4.2t models the charge level L, as a percentage, of a laptop battery after t hours of use. Which of the following is the best interpretation of the number 4.2 in this context?
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Why D is right
In the equation L=95−4.2t, the coefficient 4.2 is multiplied by t (time in hours) and subtracted from the initial charge. This represents the rate at which the battery loses charge per hour.
Why the others are wrong
AThis interprets 4.2 as the starting charge level, which is actually represented by the constant 95.
BThis assigns the wrong sign to 4.2; the negative sign in the equation indicates the charge is decreasing, not increasing.
CThis confuses the rate (percentage points per hour) with the time variable t itself.
Question 13Medium
What is the value of x in the equation 4(x+3)=2(3x − 5)?
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Why D is right
Expanding both sides gives 4x+12=6x − 10. Subtracting 4x from both sides yields 12=2x − 10. Adding 10 to both sides gives 22=2x, so x=11.
Why the others are wrong
AThis results from an error in sign when isolating the variable or combining constants.
BThis results from incorrectly manipulating terms or coefficients during the solving process.
CThis is the value of 2x rather than x, resulting from failing to complete the final division step.
Question 14Medium
The equation T=72+3.5m models the temperature T, in degrees Fahrenheit, of a liquid after being heated for m minutes. Which of the following is the best interpretation of the number 72 in this context?
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Why C is right
In the equation T=72+3.5m, the constant term 72 represents the value of T when m=0. This is the initial temperature of the liquid before any heating occurs.
Why the others are wrong
AThis interprets 72 as the rate of change, which is actually represented by the coefficient 3.5.
BThis incorrectly treats 72 as a result of some calculation involving 3.5 rather than as the initial constant value.
DThis assigns the wrong sign to 72; the positive constant indicates the starting temperature, not a decreasing value.
Question 15Medium
The equation V=800−60d models the volume V, in gallons, of water in a tank after d days. Which of the following is the best interpretation of the number 800 in this context?
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Why A is right
In the equation V=800−60d, the constant term 800 is the value of V when d=0. This represents the initial volume of water in the tank before any draining occurs.
Why the others are wrong
BThis interprets 800 as the rate of change, which is actually represented by the coefficient 60.
CThis confuses the initial volume with the time variable d.
DThis assigns the wrong sign to 800; the constant represents the starting volume, and the negative sign on 60d shows the volume is decreasing, not increasing.
Question 16Medium
The equation B=5000+250w models the balance B, in dollars, in a savings account after w weeks. Which of the following is the best interpretation of the number 250 in this context?
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Why A is right
In the equation B=5000+250w, the coefficient 250 is multiplied by w (the number of weeks) and added to the initial balance. This represents the weekly deposit amount.
Why the others are wrong
BThis interprets 250 as the starting balance, which is actually represented by the constant 5000.
CThis incorrectly treats 250 as a result involving the constant 5000 rather than as the rate of increase per week.
DThis assigns the wrong sign to 250; the positive coefficient indicates deposits (additions), not withdrawals.
Question 17Medium
What is the value of x in the equation 2(3x − 5) = 4(x+3)?
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Why C is right
Expanding both sides gives 6x−10=4x+12. Subtracting 4x from both sides yields 2x−10=12. Adding 10 to both sides gives 2x=22, so x=11.
Why the others are wrong
AThis results from a sign error when moving terms between sides of the equation.
BThis results from incorrectly dividing or using the wrong coefficient in the final step.
DThis results from forgetting to divide by 2 in the final step.
Question 18Medium
What is the value of x in the equation 5(3x − 2) = 10(x+1)?
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Why C is right
Expanding both sides gives 15x−10=10x+10. Subtracting 10x from both sides yields 5x−10=10. Adding 10 to both sides gives 5x=20, so x=4.
Why the others are wrong
AThis results from a sign error when isolating x.
BThis results from using an incorrect coefficient during the final division.
DThis results from forgetting to divide by 5 after obtaining 5x = 20.
What to do after medium
Medium is the tier that decides most scores. If these are landing, the hard set is where the remaining points are.
Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.