Using the properties of equality, solve the equation 14(8−16g)+8=g .(1 point) The solution to the equation is g= .

1 answer

To solve the equation \( 14(8 - 16g) + 8 = g \), we will use the properties of equality step-by-step:

  1. First, distribute \( 14 \) inside the parentheses: \[ 14 \cdot 8 - 14 \cdot 16g + 8 = g \] This simplifies to: \[ 112 - 224g + 8 = g \]

  2. Combine the constant terms on the left side: \[ 112 + 8 - 224g = g \] Which simplifies to: \[ 120 - 224g = g \]

  3. Next, add \( 224g \) to both sides to get all terms involving \( g \) on one side: \[ 120 = g + 224g \] This simplifies to: \[ 120 = 225g \]

  4. Now, isolate \( g \) by dividing both sides by \( 225 \): \[ g = \frac{120}{225} \]

  5. Simplify \( \frac{120}{225} \): \[ g = \frac{120 \div 15}{225 \div 15} = \frac{8}{15} \]

Thus, the solution to the equation is \[ g = \frac{8}{15}. \]