Sure! Let's solve each equation step-by-step.
### Part a) [tex]\( 2(5x - 3) = 24 \)[/tex]
1. Expand the equation: Use the distributive property to eliminate the parentheses.
[tex]\[
2 \cdot (5x - 3) = 24 \implies 2 \cdot 5x - 2 \cdot 3 = 24 \implies 10x - 6 = 24
\][/tex]
2. Isolate the term with the variable: Add 6 to both sides of the equation to move the constant term to the right-hand side.
[tex]\[
10x - 6 + 6 = 24 + 6 \implies 10x = 30
\][/tex]
3. Solve for [tex]\( x \)[/tex]: Divide both sides of the equation by 10 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{30}{10} \implies x = 3.0
\][/tex]
So the solution for part [tex]\( a \)[/tex] is:
[tex]\[
x = 3.0
\][/tex]
### Part b) [tex]\( 5(2x + 1) = 50 \)[/tex]
1. Expand the equation: Again, use the distributive property to eliminate the parentheses.
[tex]\[
5 \cdot (2x + 1) = 50 \implies 5 \cdot 2x + 5 \cdot 1 = 50 \implies 10x + 5 = 50
\][/tex]
2. Isolate the term with the variable: Subtract 5 from both sides of the equation to move the constant term to the right-hand side.
[tex]\[
10x + 5 - 5 = 50 - 5 \implies 10x = 45
\][/tex]
3. Solve for [tex]\( x \)[/tex]: Divide both sides of the equation by 10 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{45}{10} \implies x = 4.5
\][/tex]
So the solution for part [tex]\( b \)[/tex] is:
[tex]\[
x = 4.5
\][/tex]
In summary:
- The solution for part [tex]\( a \)[/tex] is [tex]\( x = 3.0 \)[/tex].
- The solution for part [tex]\( b \)[/tex] is [tex]\( x = 4.5 \)[/tex].
