Using the properties of equality, solve the equation 14(8−16g)+8=g

Question

.(1 point)
The solution to the equation is g=

Answer 1

To solve the equation \( 14(8 - 16g) + 8 = g \), we will follow the steps systematically.

1. Distribute \( 14 \) in the equation: \[ 14 \cdot 8 - 14 \cdot 16g + 8 = g \] \[ 112 - 224g + 8 = g \]

2. Combine like terms on the left side: \[ 120 - 224g = g \]

3. Add \( 224g \) to both sides to get all \( g \) terms on one side: \[ 120 = g + 224g \] \[ 120 = 225g \]

4. Divide both sides by \( 225 \): \[ g = \frac{120}{225} \]

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

Thus, the solution to the equation is: \[ \boxed{\frac{8}{15}} \]

Answer 2

you are wrong

Answer 3

Let's go through the equation step by step again to make sure we find the correct solution.

Given the equation: \[ 14(8 - 16g) + 8 = g \]

1. Distribute \(14\) across \((8 - 16g)\): \[ 14 \cdot 8 - 14 \cdot 16g + 8 = g \] \[ 112 - 224g + 8 = g \]

2. Combine like terms on the left side: \[ 120 - 224g = g \]

3. Add \(224g\) to both sides to isolate \(g\): \[ 120 = g + 224g \] \[ 120 = 225g \]

4. Divide both sides by \(225\): \[ g = \frac{120}{225} \]

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

After double-checking my calculations, the solution appears to still be: \[ g = \frac{8}{15} \]

If there's a specific part you'd like me to recheck or clarify, please let me know!