Questions: Solve. 2(4y+5)=34

Transcript text: Solve. \[ 2(4 y+5)=34 \]

Solution

Solution Steps

To solve the equation \(2(4y + 5) = 34\), we need to first distribute the 2 across the terms inside the parentheses. This will give us a linear equation in the form of \(ay + b = c\). We then isolate the variable \(y\) by performing inverse operations: subtracting the constant term from both sides and then dividing by the coefficient of \(y\).

Step 1: Distribute the Constant

Start by distributing the 2 across the terms inside the parentheses in the equation \(2(4y + 5) = 34\). This results in: \[ 8y + 10 = 34 \]

Step 2: Isolate the Variable Term

Subtract 10 from both sides of the equation to isolate the term with the variable: \[ 8y = 34 - 10 \] \[ 8y = 24 \]

Step 3: Solve for \(y\)

Divide both sides by 8 to solve for \(y\): \[ y = \frac{24}{8} \] \[ y = 3 \]