Question 257·Medium·Math

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If $3(2y - 4) = 5y + 6$ , what is the value of $y$ ?

A linear equation can have its variable on both sides. Distribute across the parentheses, then collect the variable terms on one side and leave the variable alone. You can check your result by entering the original equation as a regression in Desmos. Multiply the outside number by every term inside the parentheses; dropping the constant changes the equation.

Hints

Hint 1
To distribute means to multiply the number outside parentheses by each term inside. The $3$ multiplies both $2y$ and $-4$ . What does the left side become when you include both products?
Hint 2
To isolate $y$ means to leave it alone on one side. Once the parentheses are gone, subtract $5y$ from both sides. What operation will then remove the constant beside $y$ ?

Step-by-step

Solve by hand, then check in Desmos
Step 1
Distribute the 3
To distribute is to multiply each term inside the parentheses by the outside number. That includes $-4$ , so $3(-4)=-12$ . Distribute across both terms:
$6y-12=5y+6.$
Step 2
Collect the variable terms
To isolate $y$ is to leave it alone on one side. Subtract $5y$ from both sides so the equation stays equal:
$y-12=6.$
Step 3
Remove the constant
Undo the $-12$ by adding $12$ to both sides:
$y=6+12.$
Step 4
Check the original equation
Type the original equation in Desmos with $y$ replaced by $y_1$ and $=$ replaced by $\sim$ : $3(2y_1-4)\sim5y_1+6$ . The $\sim$ asks Desmos to find a value that makes both sides equal. Under PARAMETERS, it reports $y_1=18$ , matching $6+12$ . So the value of $y$ is $18$ . Choice D.

Question 257·Medium·Math

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Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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