Question 940·Easy·Math

0 / 2000

$4(a - b) = 2c + 8$

The equation above relates the variables $a$ , $b$ , and $c$ . Which equation correctly expresses $c$ in terms of $a$ and $b$ ?

The phrase “express $c$ in terms of $a$ and $b$ ” signals rearranging a formula: get $c$ alone while leaving $a$ and $b$ as letters. Undo the operations around $c$ in reverse order, keeping both sides balanced. Desmos can check choices at sample values, but hand algebra proves the relationship for every value. Watch out for dividing only part of a side.

Hints

Hint 1
In a formula, “in terms of $a$ and $b$ ” means $c$ must stand alone while $a$ and $b$ remain as letters. What should you do to both sides to remove the $+8$ beside $2c$ ?
Hint 2
After removing $8$ , the right side still has a coefficient, a number multiplying $c$ . To undo multiplication, divide both whole sides by that coefficient. Why can't you divide one term on the left?

Step-by-step

Approach 1: Rearrange the formula

Step 1
Remove the added 8
No Desmos needed. Rearranging the letters directly proves the formula for every value. The question asks for $c$ , so leave $a$ and $b$ as letters. Subtract $8$ from both sides to remove the $+8$ beside $2c$ :
$4(a-b)-8=2c+8-8$ $4(a-b)-8=2c$
Step 2
Get c alone
The coefficient of $c$ , the number multiplying it, is $2$ . Divide each whole side by $2$ , including the $-8$ on the left:
$\frac{4(a-b)-8}{2}=\frac{2c}{2}$ $2(a-b)-4=c$
Write $c$ on the left:
$c=2(a-b)-4$
A move on an equation applies to both whole sides. So $c$ in terms of $a$ and $b$ is $2(a-b)-4$ . Choice D.

Approach 2: Check the choices with Desmos

Step 1
Find c for sample values
Pick $a=3$ and $b=1$ to make a quick test case. Type those values, then type the given equation with $\sim$ in place of $=$ and $c_1$ in place of $c$ . This regression asks Desmos to find $c_1$ ; it reports $c_1=0$ under PARAMETERS.
Step 2
Test every choice
Keep those lines and type the four proposed expressions. Desmos shows $8$ , $-4$ , $4$ , and $0$ , in that order. Only $2(a-b)-4$ gives $0$ , the value required by the original equation for this test case. A single test can rule choices out; the rearrangement above proves the formula for all $a$ and $b$ . So $c=2(a-b)-4$ . Choice D.

Lessons that teach this

SAT Advanced AlgebraIntermediateCoreRearrange nonlinear formulas

Question 940·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

Lessons that teach this