Question
Solve the equation and check the result. \[ 16 y-8(3 y-6)=-72 \] SUBMIT ANSWER
Ask by Munoz Turner. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y=15 \)
Solution
Solve the equation \( 16y-8(3y-6)=-72 \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(16y-8\left(3y-6\right)=-72\)
- step1: Move the expression to the left side:
\(16y-8\left(3y-6\right)-\left(-72\right)=0\)
- step2: Remove the parentheses:
\(16y-8\left(3y-6\right)+72=0\)
- step3: Calculate:
\(-8y+120=0\)
- step4: Move the constant to the right side:
\(-8y=0-120\)
- step5: Remove 0:
\(-8y=-120\)
- step6: Change the signs:
\(8y=120\)
- step7: Divide both sides:
\(\frac{8y}{8}=\frac{120}{8}\)
- step8: Divide the numbers:
\(y=15\)
The solution to the equation \(16y-8(3y-6)=-72\) is \(y=15\).
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Simplify this solution Extra Insights
Let's solve the equation step by step: Starting with the equation: \[ 16y - 8(3y - 6) = -72 \] Step 1: Distribute \( -8 \) into \( (3y - 6) \): \[ 16y - 24y + 48 = -72 \] Step 2: Combine like terms: \[ -8y + 48 = -72 \] Step 3: Subtract \( 48 \) from both sides: \[ -8y = -120 \] Step 4: Divide by \( -8 \): \[ y = 15 \] Now, let's check the result by substituting \( y = 15 \) back into the original equation: \[ 16(15) - 8(3(15) - 6) = -72 \] \[ 240 - 8(45 - 6) = -72 \] \[ 240 - 8(39) = -72 \] \[ 240 - 312 = -72 \] \[ -72 = -72 \] Since both sides are equal, the solution is correct. The answer is: \[ y = 15 \]
