Sure, let’s solve these equations step-by-step.
### Part (a)
Given the equation:
[tex]\[ 2(5x - 3) = 24 \][/tex]
1. Distribute the 2 across the terms inside the parentheses:
[tex]\[ 2 \cdot 5x - 2 \cdot 3 = 24 \][/tex]
[tex]\[ 10x - 6 = 24 \][/tex]
2. Isolate the variable term (10x) by adding 6 to both sides of the equation:
[tex]\[ 10x - 6 + 6 = 24 + 6 \][/tex]
[tex]\[ 10x = 30 \][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 10:
[tex]\[ x = \frac{30}{10} \][/tex]
[tex]\[ x = 3 \][/tex]
So, the solution for part (a) is:
[tex]\[ x = 3 \][/tex]
### Part (b)
Given the equation:
[tex]\[ 5(2x + 1) = 50 \][/tex]
1. Distribute the 5 across the terms inside the parentheses:
[tex]\[ 5 \cdot 2x + 5 \cdot 1 = 50 \][/tex]
[tex]\[ 10x + 5 = 50 \][/tex]
2. Isolate the variable term (10x) by subtracting 5 from both sides of the equation:
[tex]\[ 10x + 5 - 5 = 50 - 5 \][/tex]
[tex]\[ 10x = 45 \][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 10:
[tex]\[ x = \frac{45}{10} \][/tex]
[tex]\[ x = 4.5 \][/tex]
So, the solution for part (b) is:
[tex]\[ x = 4.5 \][/tex]
Thus, the solutions are:
- For part (a), [tex]\( x = 3 \)[/tex]
- For part (b), [tex]\( x = 4.5 \)[/tex]
