Question 994·Easy·Math

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$5(x - 2) = 3y + 10$

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

The phrase “express $x$ in terms of $y$ ” asks you to solve for a variable: leave $x$ alone while $y$ stays in the formula. A positive test value in Desmos can catch a wrong choice, but one test cannot prove a formula works for every $y$ . To get the formula, distribute across both terms, then keep the equation balanced as you isolate $x$ .

Hints

Hint 1
Choose a positive test value for $y$ , such as $5$ . A correct formula must give the same $x$ that the original equation gives. What does Desmos find when you substitute that value?
Hint 2
To distribute the $5$ , multiply both terms inside the parentheses by it. In particular, $5$ multiplies $-2$ as well as $x$ . What does the left side become?
Hint 3
Use the balance rule: doing the same operation to both sides keeps an equation true. Once you have $5x-10$ , what must you add to remove the $-10$ ?

Step-by-step

Check a value, then isolate x
Step 1
Find a test value in Desmos
Choose $y=5$ , which meets the positive-number condition. Type $5(x_1-2)\sim3(5)+10$ : $x_1$ tells Desmos which value to find, and $\sim$ tells it to fit the two sides. Under PARAMETERS, Desmos shows $x_1=7$ . Any correct formula must give $7$ when $y=5$ , but one test is a check, not proof for every $y$ .
Step 2
Distribute the 5
Multiply $5$ by each term in $x-2$ ; it turns $-2$ into $-10$ :
$5x-10=3y+10.$
Step 3
Remove the minus 10
Add $10$ to both sides so that $5x$ stands alone on the left: $5x=3y+20$ . The $20$ is the given $10$ plus the $10$ you added.
Step 4
Get x alone
Divide both sides by $5$ : $x=\frac{3y+20}{5}$ . This expresses $x$ in terms of $y$ , as requested. Choice D.

Question 994·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this