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

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SAT Nonlinear Equations & Systems Question 13 | Free SAT Prep | Aniko

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Question 13·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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

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

When you are asked to "express one variable in terms of others," your goal is to isolate that variable step by step using inverse operations: move constants first (by adding or subtracting on both sides), then undo multiplication or division (by dividing or multiplying every term on one side). After isolating the variable, simplify carefully—especially when dividing—making sure every term is affected, then factor if needed so your result matches the form of the answer choices. Staying systematic about each operation reduces sign and distribution mistakes and makes these problems quick to solve.

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Focus on isolating $c$

You want an equation that has $c$ alone on one side. Which terms need to be moved away from $c$ in the original equation?

Remove the constant term first

In $4(a - b) = 2c + 8$ , what operation will get rid of the $+8$ on the right side? Do that operation to both sides.

Be careful when dividing

After you isolate $2c$ , you will need to divide by $2$ . Make sure you divide every term on the other side by $2$ , not just one part.

Desmos Guide

Pick sample values for $a$ and $b$

In Desmos, type values like a = 5 and b = 1 (or use sliders for a and b). These will let you test which expression for c matches the original equation.

Compute $c$ from the original equation

Enter the original equation rewritten to solve numerically for c, for example: 4(a - b) = 2c + 8. Then, for your chosen a and b, adjust c (or use Desmos’s numeric solver feature if available) until the left and right sides are equal. Note down this numeric value of c.

Test each option numerically

For each answer choice, enter its expression into Desmos as a separate line (e.g., c1 = 2(a - b) + 4, c2 = 2(a - b) - 8, etc.). With the same a and b values, compare the numeric values of c1, c2, c3, and c4 to the $c$ you found from the original equation. The correct choice is the one whose computed value of c matches exactly.

Step-by-step Explanation

Isolate the term with $c$

Start with the given equation:

4(a - b) = 2c + 8

To move the constant term $8$ away from $c$ , subtract $8$ from both sides:

4(a - b) - 8 = 2c

Now the right side has only the term involving $c$ .

Solve for $c$ by dividing

You now have:

4(a - b) - 8 = 2c

To isolate $c$ , divide both sides of the equation by $2$ :

\frac{4(a - b) - 8}{2} = c

This division applies to both terms in the numerator: $4(a - b)$ and $-8$ .

Simplify the expression

Simplify the fraction:

$\dfrac{4(a - b)}{2} = 2(a - b)$
$\dfrac{-8}{2} = -4$

So the equation becomes:

c = 2(a - b) - 4

This matches the correct choice.

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Step-by-step Explanation

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Step-by-step Explanation