Sure, let's solve each part step-by-step.
### Part A: [tex]\( 3x - 5 = 19 \)[/tex]
1. Isolate the term with [tex]\(x\)[/tex]: To do this, we need to get rid of the constant term on the left side. We add 5 to both sides of the equation:
[tex]\[
3x - 5 + 5 = 19 + 5
\][/tex]
[tex]\[
3x = 24
\][/tex]
2. Solve for [tex]\(x\)[/tex]: Now, we need to isolate [tex]\(x\)[/tex]. Since [tex]\(x\)[/tex] is multiplied by 3, we divide both sides of the equation by 3:
[tex]\[
x = \frac{24}{3}
\][/tex]
[tex]\[
x = 8
\][/tex]
So, the solution for Part A is:
[tex]\[
x = 8
\][/tex]
### Part B: [tex]\(\frac{2}{3}(6 + x) = 9\)[/tex]
1. Eliminate the fraction: To make things simpler, we'll multiply both sides of the equation by the reciprocal of [tex]\(\frac{2}{3}\)[/tex], which is [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\frac{3}{2} \cdot \frac{2}{3}(6 + x) = 9 \cdot \frac{3}{2}
\][/tex]
[tex]\[
6 + x = 13.5
\][/tex]
2. Solve for [tex]\(x\)[/tex]: Now we need to isolate [tex]\(x\)[/tex]. We subtract 6 from both sides of the equation:
[tex]\[
6 + x - 6 = 13.5 - 6
\][/tex]
[tex]\[
x = 7.5
\][/tex]
So, the solution for Part B is:
[tex]\[
x = 7.5
\][/tex]
Thus, the solutions for the equations are:
- Part A: [tex]\(x = 8\)[/tex]
- Part B: [tex]\(x = 7.5\)[/tex]
