25 hard SAT Linear equations · one variable questions

If 9 - $2(x - 5) = 3x + 4$, what is the value of $5x - 6$?

• A$3$
• B$21$
• C$9$
• D$4$

$8(3 - nx) + 24x = 60$ In the given equation, n is a constant. The equation has no solution. What is the value of n?

• A$-3$
• B$5$
• C$8$
• D$3$

A reservoir contains 6400 gallons of water. Due to evaporation, the reservoir loses 2.5% of its current volume each day, but it also receives 140 gallons of water each day from rainfall. Which equation best represents the amount of water w, in gallons, in the reservoir after d days, assuming the percentage loss applies to the volume at the start of each day?

• A$w = 6400(0.975)^{d} + 140d$
• B$w = 6400(0.975)^{d} - 140d$
• C$w = 6400 - 160d + 140d$
• D$w = 6400(1.025)^{d} + 140d$

The equation $A = 3500 - 125m$ models the amount A, in dollars, remaining in an account m months after a withdrawal plan begins. Which of the following is the best interpretation of the number 125 in this context?

• AThe amount, in dollars, in the account when the withdrawal plan begins
• BThe rate of decrease, in dollars per month, of the account balance
• CThe rate of increase, in dollars per month, of the account balance
• DThe amount, in dollars, remaining in the account after 125 months

$8(2x + 3) - 5x = kx + 24$ In the given equation, k is a constant. The equation has infinitely many solutions. What is the value of k?

• A$16$
• B$-11$
• C$11$
• D$21$

If $3(2x - 5) = 4x + 7$, what is the value of $x + 8$?

• A$11$
• B$19$
• C$-5$
• D$5.5$

$2(6x + 11) = 4(px + 7) + 4x$ In the given equation, p is a constant. The equation has no solution. What is the value of p?

• A$6$
• B$2$
• C$-2$
• D$4$

A savings account starts with a balance of $2500. Each month, $180 is automatically deposited into the account, and the account earns interest equal to 0.4% of the balance at the beginning of that month. Which equation best represents the balance b, in dollars, after m months?

• A$b = 2500(1.004)^{m} + 180m$
• B$b = 2500 + 180m + 10m$
• C$b = 2500(0.996)^{m} + 180m$
• D$b = 2500(1.004)^{m} - 180m$

The equation $W = 95 + 6.8d$ models the weight W, in pounds, of a calf d days after birth. Which of the following is the best interpretation of the number 6.8 in this context?

• AThe weight, in pounds, of the calf at birth
• BThe rate of decrease, in pounds per day, of the calf's weight
• CThe rate of increase, in pounds per day, of the calf's weight
• DThe weight, in pounds, of the calf after 6 or 8 days

$7(2x - 5) = kx - 35$ In the given equation, k is a constant. The equation has infinitely many solutions. What is the value of k?

• A$7$
• B$-14$
• C$35$
• D$14$

If $6(x - 2) = 3 (x + 4)$, what is the value of $4x + 1$?

• A$8$
• B$33$
• C$31$
• D$37$

$4(3x + 8) - 9x = 15px - 7$ In the given equation, p is a constant. The equation has no solution. What is the value of p?

• A$\displaystyle \frac{4}{5}$
• B$\displaystyle \frac{1}{5}$
• C$\displaystyle -\frac{1}{5}$
• D$5$

A cell phone plan charges a monthly fee of $35 plus $0.08 per text message sent. Another plan charges a monthly fee of $50 but only $0.03 per text message sent. For how many text messages in a month would the total cost be the same for both plans?

• A$187$
• B$250$
• C$300$
• D$428$

The equation $h = 240 - 15t$ models the height h, in feet, of a hot air balloon t minutes after it begins descending. Which of the following is the best interpretation of the number 15 in this context?

• AThe height, in feet, of the balloon after 1 minute
• BThe rate of increase, in feet per minute, of the balloon's height
• CThe initial height, in feet, of the balloon when it begins descending
• DThe rate of decrease, in feet per minute, of the balloon's height

$4(3x + 5) = nx + 20$ In the given equation, n is a constant. The equation has infinitely many solutions. What is the value of n?

• A$3$
• B$-12$
• C$4$
• D$12$

If $8x - 5 (x - 3) = 33$, what is the value of $2x - 9$?

• A$3$
• B$6$
• C$21$
• D$5$

$3(4x - 9) = kx + 15$ In the given equation, k is a constant. The equation has no solution. What is the value of k?

• A$-12$
• B$3$
• C$12$
• D$4$

The equation $T = 18 + 2.5n$ models the total time T, in hours, required to complete a project with n workers. Which of the following is the best interpretation of the number 2.5 in this context?

• AThe time, in hours, required before any workers begin
• BThe decrease, in hours, in total time for each additional worker
• CThe increase, in hours, in total time for each additional worker
• DThe total time, in hours, required for 2 or 3 workers

$8(2x + 5) - 6kx = 40 + 10x$ In the given equation, k is a constant. The equation has infinitely many solutions. What is the value of k?

• A$-1$
• B$\displaystyle \frac{3}{2}$
• C$1$
• D$2$

If $3(x + 7) = 2 (x + 14)$, what is the value of $4x - 2$?

• A$7$
• B$26$
• C$30$
• D$22$

$6x - 9 = px + 15$ In the given equation, p is a constant. The equation has no solution. What is the value of p?

• A$-6$
• B$9$
• C$6$
• D$3$

The equation $D = 520 - 3.2t$ models the distance D, in miles, between two trains t minutes after they begin moving apart. Which of the following is the best interpretation of the number 520 in this context?

• AThe distance, in miles, between the trains after 1 minute
• BThe rate of increase, in miles per minute, of the distance between the trains
• CThe initial distance, in miles, between the trains when they begin moving apart
• DThe rate of decrease, in miles per minute, of the distance between the trains

$9x + 27 = 3(px + 9)$ In the given equation, p is a constant. The equation has infinitely many solutions. What is the value of p?

• A$9$
• B$27$
• C$3$
• D$-3$

$7(kx - 4) = 21x + 35$ In the given equation, k is a constant. The equation has no solution. What is the value of k?

• A$-3$
• B$5$
• C$3$
• D$7$

$5(2 + kx) - 15x = 42$ In the given equation, k is a constant. The equation has no solution. What is the value of k?

• A$7$
• B$5$
• C$3$
• D$-3$