Question

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Part 1
Solve the equation. Check your solution.
5gplus4​(negative 8plus3​g)equals1minusg
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Part 1
gequals
  
enter your response here ​(Type an integer or a simplified​ fraction.)

Answer 1

To solve the equation \( 5g + 4(-8 + 3g) = 1 - g \), we will simplify both sides step by step.

1. Distribute \( 4 \) to the terms in the parentheses on the left side:

\[
5g + 4(-8) + 4(3g) = 1 - g
\]

This simplifies to:

\[
5g - 32 + 12g = 1 - g
\]

2. Combine like terms on the left side:

\[
(5g + 12g) - 32 = 1 - g
\]

Thus, we have:

\[
17g - 32 = 1 - g
\]

3. Now, add \( g \) to both sides to get all \( g \) terms on one side:

\[
17g + g - 32 = 1
\]

This simplifies to:

\[
18g - 32 = 1
\]

4. Next, add \( 32 \) to both sides:

\[
18g = 1 + 32
\]

So:

\[
18g = 33
\]

5. Now, divide both sides by \( 18 \):

\[
g = \frac{33}{18}
\]

This can be simplified:

\[
g = \frac{11}{6}
\]

Now, let's check our solution by substituting \( g = \frac{11}{6} \) back into the original equation.

\[
5\left(\frac{11}{6}\right) + 4(-8 + 3\left(\frac{11}{6}\right)) = 1 - \left(\frac{11}{6}\right)
\]

Calculating the left side:

1. Calculate \( 5\left(\frac{11}{6}\right) \):

\[
5 \times \frac{11}{6} = \frac{55}{6}
\]

2. Calculate \( 3\left(\frac{11}{6}\right) \):

\[
3 \times \frac{11}{6} = \frac{33}{6}
\]

3. Now calculate the expression inside the parentheses:

\[
-8 + \frac{33}{6} = -\frac{48}{6} + \frac{33}{6} = -\frac{15}{6}
\]

4. Multiply by \( 4 \):

\[
4 \times -\frac{15}{6} = -\frac{60}{6} = -10
\]

5. Add this to \( \frac{55}{6} \):

\[
\frac{55}{6} - 10 = \frac{55}{6} - \frac{60}{6} = -\frac{5}{6}
\]

Now calculating the right side:

\[
1 - \frac{11}{6} = \frac{6}{6} - \frac{11}{6} = -\frac{5}{6}
\]

Since both sides are equal, the solution is confirmed.

Thus, the solution to the equation is:

\[
\boxed{\frac{11}{6}}
\]