SAT Linear equations · one variable

Solve for x — and read carefully what they actually ask for.

6% of MathMath · Algebra4 question types
~3per test

How to score it

  • Solve fully, then re-read the question — they often ask for x − 3 or 2x, not x.
  • Underline exactly what's being asked before you bubble.
  • In context problems, translate one phrase at a time into the equation.

Common traps

  • Asks for “x − 3” but gives you x as a choice.
  • Sign error from moving a term across the equals sign.
  • “Infinitely many solutions” = coefficient-matching, not solving.

The 4 question types, with real examples

Solve, then evaluate an expression

“If [linear equation], what is the value of [expression in x]?”

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From the question bankMedium

If 6x−14=4x+86x - 14 = 4x + 8, what is the value of x−6x - 6?

  • A1717
  • B1111
  • C1010
  • D55✓
Why D

Subtracting 4x from both sides gives 2x−14=82x - 14 = 8, so 2x=222x = 22 and x=11x = 11. Therefore, x−6=11−6=5x - 6 = 11 - 6 = 5.

Context → write or solve a linear equation

“[Rate / savings / depletion scenario] — how many … ?”

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From the question bankMedium

The equation C=280+6.5hC = 280 + 6.5h represents the total cost C, in dollars, to rent a venue for h hours.

What is the meaning of the 6.5 in this equation?

  • AThe cost per hour to rent the venue✓
  • BThe total cost to rent the venue
  • CThe number of hours the venue can be rented
  • DThe cost for 280 hours of rental
Why A

In the linear equation C=280+6.5hC = 280 + 6.5h, the coefficient 6.5 multiplies the number of hours h, representing the rate of cost increase per hour, which is $6.50 per hour.

Interpret a slope or intercept in context

“Which is the best interpretation of [number] in this context?”

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From the question bankMedium

The equation C=45+12hC = 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?

  • AThe cost, in dollars, to rent the bicycle for one hour
  • BThe initial cost, in dollars, to rent the bicycle before any hours are counted✓
  • CThe total cost, in dollars, to rent the bicycle for 12 hours
  • DThe cost, in dollars, that decreases for each hour the bicycle is rented
Why B

In the equation C=45+12hC = 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.

Solve given equation (display form, no context)

“[eq] (centered). What value of x is the solution to the given equation?”

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From the question bankMedium

What is the value of x in the equation 3(x+4)=2(x+9)3(x + 4) = 2 (x + 9)?

  • A22
  • B66✓
  • C−6-6
  • D33
Why B

Expandingbothsidesgives3x+12=2x+18.Subtracting2xfrombothsidesyieldsx+12=18.Subtracting12frombothsidesgivesx=6.Expanding both sides gives 3x + 12 = 2x + 18. Subtracting 2x from both sides yields x + 12 = 18. Subtracting 12 from both sides gives x = 6.

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