Questions: 8(2y+5)=12y-(2y+14)

Transcript text: 31. $8(2 y+5)=12 y-(2 y+14)$

Solution

Step 1: Expand the left side of the equation

Expand $ 8(2y + 5) $ using the distributive property: \[ 8(2y + 5) = 16y + 40 \]

Step 2: Expand the right side of the equation

Expand $ 12y - (2y + 14) $ by distributing the negative sign: \[ 12y - (2y + 14) = 12y - 2y - 14 = 10y - 14 \]

Step 3: Rewrite the equation with expanded terms

Substitute the expanded forms back into the original equation: \[ 16y + 40 = 10y - 14 \]

Step 4: Move all $ y $-terms to one side and constants to the other

Subtract $ 10y $ from both sides: \[ 16y - 10y + 40 = -14 \] Simplify: \[ 6y + 40 = -14 \]

Step 5: Solve for $ y $

Subtract $ 40 $ from both sides: \[ 6y = -14 - 40 \] Simplify: \[ 6y = -54 \] Divide both sides by $ 6 $: \[ y = -9 \]

$\boxed{y = -9}$

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