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Persevere with Problems: Solve each equation.

a. [tex]2 \cdot 5(x+4) + x = 38[/tex]

b. [tex]6.1(x-2) + x = 51.7[/tex]

Answer :

Certainly! Let's solve each equation step-by-step:

### Equation (a): [tex]\(2 \cdot 5(x+4) + x = 38\)[/tex]

1. Distribute: First, distribute [tex]\( 2 \cdot 5 \)[/tex] across the term [tex]\((x + 4)\)[/tex].
[tex]\[
10(x + 4) + x = 38
\][/tex]

2. Expand: Distribute the 10 into the parentheses.
[tex]\[
10x + 40 + x = 38
\][/tex]

3. Combine Like Terms: Combine the [tex]\( x \)[/tex] terms on the left side.
[tex]\[
11x + 40 = 38
\][/tex]

4. Isolate the Variable Term: Subtract 40 from both sides to isolate the terms with [tex]\( x \)[/tex].
[tex]\[
11x = 38 - 40
\][/tex]
[tex]\[
11x = -2
\][/tex]

5. Solve for [tex]\( x \)[/tex]: Divide both sides by 11 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{-2}{11}
\][/tex]

### Equation (b): [tex]\(6.1(x-2) + x = 51.7\)[/tex]

1. Distribute: Expand the term [tex]\( 6.1(x - 2) \)[/tex].
[tex]\[
6.1x - 12.2 + x = 51.7
\][/tex]

2. Combine Like Terms: Combine the [tex]\( x \)[/tex] terms on the left side.
[tex]\[
7.1x - 12.2 = 51.7
\][/tex]

3. Isolate the Variable Term: Add 12.2 to both sides to isolate the terms with [tex]\( x \)[/tex].
[tex]\[
7.1x = 51.7 + 12.2
\][/tex]
[tex]\[
7.1x = 63.9
\][/tex]

4. Solve for [tex]\( x \)[/tex]: Divide both sides by 7.1 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{63.9}{7.1}
\][/tex]

### Solutions:
- For equation (a), [tex]\( x = \frac{-2}{11} \)[/tex], which is approximately [tex]\(-0.1818\)[/tex].
- For equation (b), [tex]\( x = 9.0 \)[/tex].

These are the solutions for each equation.

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