Ask a New Question
Menu

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

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

5 answers

To solve the equation \( 14(8 - 16g) + 8 = g \), we will follow these steps using the properties of equality:

  1. Start with the given equation: \[ 14(8 - 16g) + 8 = g \]

  2. Distribute the \( 14 \) on the left side: \[ 14 \cdot 8 - 14 \cdot 16g + 8 = g \] This simplifies to: \[ 112 - 224g + 8 = g \]

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

  4. Add \( 224g \) to both sides to get all terms involving \( g \) on one side: \[ 120 = g + 224g \] Simplifying this gives: \[ 120 = 225g \]

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

  6. Simplify the fraction: \[ g = \frac{8}{15} \]

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

the answer is 8/15?

Yes, that's correct! The solution to the equation \( 14(8 - 16g) + 8 = g \) simplifies to \( g = \frac{8}{15} \). If you have any further questions about this problem or need additional assistance, feel free to ask!

its wrong tho

Let's carefully solve the equation \( 14(8 - 16g) + 8 = g \) step by step to find the correct solution.

Starting with the equation:

\[ 14(8 - 16g) + 8 = g \]

  1. Distribute \( 14 \) on the left side:

\[ 14 \cdot 8 - 14 \cdot 16g + 8 = g \]

\[ 112 - 224g + 8 = g \]

  1. Combine like terms on the left side:

\[ 120 - 224g = g \]

  1. Add \( 224g \) to both sides to get all terms involving \( g \) on one side:

\[ 120 = g + 224g \]

\[ 120 = 225g \]

  1. Now, divide both sides by \( 225 \):

\[ g = \frac{120}{225} \]

  1. Now simplify \( \frac{120}{225} \):

\[ g = \frac{120 \div 15}{225 \div 15} = \frac{8}{15} \]

So the final solution is:

\[ g = \frac{8}{15} \]

If you think there's an error, please let me know where you think the issue might be, and we can go through it again!