Certainly, let's solve each equation step by step.
### Part A: Solve [tex]\( 3x - 5 = 19 \)[/tex]
1. Isolate the variable [tex]\(x\)[/tex] by first getting rid of the constant term on the left side.
- Add 5 to both sides of the equation to move the constant term:
[tex]\[
3x - 5 + 5 = 19 + 5
\][/tex]
- This simplifies to:
[tex]\[
3x = 24
\][/tex]
2. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by the coefficient of [tex]\(x\)[/tex].
- Divide both sides by 3:
[tex]\[
x = \frac{24}{3}
\][/tex]
- Simplifying this gives:
[tex]\[
x = 8
\][/tex]
So, the solution for Part A is [tex]\( x = 8 \)[/tex].
### Part B: Solve [tex]\( \frac{2}{3}(6 + x) = 9 \)[/tex]
1. Isolate the term with [tex]\(x\)[/tex] by removing the coefficient from outside the parentheses.
- Multiply both sides of the equation by the reciprocal of [tex]\(\frac{2}{3}\)[/tex], which is [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\left(\frac{3}{2}\right) \cdot \frac{2}{3}(6 + x) = 9 \cdot \left(\frac{3}{2}\right)
\][/tex]
- Simplify the left side; the [tex]\(\frac{3}{2}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex] cancel each other out:
[tex]\[
6 + x = 13.5
\][/tex]
2. Solve for [tex]\(x\)[/tex] by isolating it on one side of the equation.
- Subtract 6 from both sides:
[tex]\[
x = 13.5 - 6
\][/tex]
- Simplify this:
[tex]\[
x = 7.5
\][/tex]
So, the solution for Part B is [tex]\( x = 7.5 \)[/tex].
In summary:
- The solution for Part A is [tex]\( x = 8 \)[/tex].
- The solution for Part B is [tex]\( x = 7.5 \)[/tex].
