Question

Solve the following linear equation.
10x+12+6x+14=−182
Solve the following linear equation.
−4 (4x+1) = 13
x=
(Note: if the answer is an infinite repeating decimal your answer must be in fraction form. So 0.333... = 1/3)

Answer 1

Let's solve each equation step by step.

### First Equation:
\[ 10x + 12 + 6x + 14 = -182 \]

1. Combine like terms:
\[ (10x + 6x) + (12 + 14) = -182 \]
\[ 16x + 26 = -182 \]

2. Subtract 26 from both sides:
\[ 16x + 26 - 26 = -182 - 26 \]
\[ 16x = -208 \]

3. Divide both sides by 16:
\[ x = \frac{-208}{16} \]
\[ x = -13 \]

### Second Equation:
\[ -4(4x + 1) = 13 \]

1. Distribute the -4:
\[ -16x - 4 = 13 \]

2. Add 4 to both sides:
\[ -16x - 4 + 4 = 13 + 4 \]
\[ -16x = 17 \]

3. Divide both sides by -16:
\[ x = \frac{17}{-16} \]
\[ x = -\frac{17}{16} \]

### Final Answers:
1. For the first equation: \( x = -13 \)
2. For the second equation: \( x = -\frac{17}{16} \)

So the answers are:
- \( x = -13 \)
- \( x = -\frac{17}{16} \)