Question 254·Easy·Advanced Math

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(x + 5)(y - 2) = 18

The equation above relates the distinct positive numbers $x$ and $y$ . Which equation correctly expresses $y$ in terms of $x$ ?

The words “express $y$ in terms of $x$ ” call for rearranging a formula: keep $x$ as a letter and get $y$ alone. Undo the operations around $y$ from the outside in. First divide by the whole factor multiplying $y-2$ , then add $2$ . Keep that $2$ outside the fraction; adding it does not change the denominator.

Hints

Hint 1
The target is $y$ , while $x$ stays in the formula. In the product $(x+5)(y-2)$ , which factor would you divide by to leave $y-2$ alone?
Hint 2
Once you have $y-2$ alone, add $2$ to both sides to get $y$ . Adding to a fraction means adding to the whole fraction, not changing its denominator.

Step-by-step

Isolate $y$
Step 1
Undo the multiplication
No Desmos needed. We need a formula for every positive $x$ , not a number from one chosen value. Because $x$ is positive, $x+5$ cannot be $0$ . Divide by the whole factor multiplying $y-2$ to leave that group alone:
$y-2=\frac{18}{x+5}.$
Step 2
Get $y$ alone
Undo the subtraction of $2$ by adding $2$ to both sides: $y=\frac{18}{x+5}+2$ . The $2$ is outside the fraction because you added it to the whole right side. This gives $y$ in terms of $x$ . Choice D.

Lessons that teach this

SAT Advanced AlgebraIntermediateCoreRearrange nonlinear formulas

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Question 254·Easy·Advanced Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

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Step-by-step

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