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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 :

Sure! Let's solve each equation step by step:

### a. [tex]\(2 \cdot 5(x+4) + x = 38\)[/tex]
1. Distribute the 2 and 5 across the parentheses:
[tex]\[
2 \cdot 5(x + 4) = 10(x + 4)
\][/tex]
This simplifies to:
[tex]\[
10x + 40
\][/tex]

2. Rewrite the equation:
[tex]\[
10x + 40 + x = 38
\][/tex]

3. Combine like terms:
[tex]\[
11x + 40 = 38
\][/tex]

4. Subtract 40 from both sides:
[tex]\[
11x = 38 - 40
\][/tex]
[tex]\[
11x = -2
\][/tex]

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

### b. [tex]\(6.1(x-2) + x = 51.7\)[/tex]
1. Distribute the 6.1 across the parentheses:
[tex]\[
6.1(x - 2) = 6.1x - 12.2
\][/tex]

2. Rewrite the equation:
[tex]\[
6.1x - 12.2 + x = 51.7
\][/tex]

3. Combine like terms:
[tex]\[
7.1x - 12.2 = 51.7
\][/tex]

4. Add 12.2 to both sides:
[tex]\[
7.1x = 51.7 + 12.2
\][/tex]
[tex]\[
7.1x = 63.9
\][/tex]

5. Divide both sides by 7.1 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{63.9}{7.1}
\][/tex]
[tex]\[
x = 9
\][/tex]

The solutions for the equations are:
a. [tex]\(x = -\frac{2}{11}\)[/tex]
b. [tex]\(x = 9\)[/tex]

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