Sure, let's solve each equation step-by-step.
### Part (a): Solve \( 2(5x - 3) = 24 \)
1. Distribute the 2 on the left side of the equation:
[tex]\[
2(5x - 3) = 2 \cdot 5x - 2 \cdot 3 = 10x - 6
\][/tex]
So the equation becomes:
[tex]\[
10x - 6 = 24
\][/tex]
2. Add 6 to both sides to isolate the term with \( x \):
[tex]\[
10x - 6 + 6 = 24 + 6
\][/tex]
Simplifying this, we get:
[tex]\[
10x = 30
\][/tex]
3. Divide both sides by 10 to solve for \( x \):
[tex]\[
x = \frac{30}{10}
\][/tex]
Hence, we find:
[tex]\[
x = 3
\][/tex]
So, the solution for part (a) is \( x = 3 \).
### Part (b): Solve \( 5(2x + 1) = 50 \)
1. Distribute the 5 on the left side of the equation:
[tex]\[
5(2x + 1) = 5 \cdot 2x + 5 \cdot 1 = 10x + 5
\][/tex]
So the equation becomes:
[tex]\[
10x + 5 = 50
\][/tex]
2. Subtract 5 from both sides to isolate the term with \( x \):
[tex]\[
10x + 5 - 5 = 50 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
10x = 45
\][/tex]
3. Divide both sides by 10 to solve for \( x \):
[tex]\[
x = \frac{45}{10}
\][/tex]
Hence, we find:
[tex]\[
x = 4.5
\][/tex]
So, the solution for part (b) is \( x = 4.5 \).
Therefore, the solutions are:
- For \( 2(5x - 3) = 24 \): \( x = 3 \)
- For \( 5(2x + 1) = 50 \): \( x = 4.5 \)
The final results are [tex]\( x = 3 \)[/tex] and [tex]\( x = 4.5 \)[/tex].
