Let's solve the equation step by step and verify our solution by substituting it back into the original equation.
Given equation:
[tex]\[ 4(2x - 4) = 22 \][/tex]
Step 1: Distribute the 4 on the left side of the equation.
[tex]\[ 4 \cdot (2x - 4) = 4 \cdot 2x - 4 \cdot 4 \][/tex]
[tex]\[ 8x - 16 = 22 \][/tex]
Step 2: To isolate the term containing [tex]\( x \)[/tex], add 16 to both sides of the equation.
[tex]\[ 8x - 16 + 16 = 22 + 16 \][/tex]
[tex]\[ 8x = 38 \][/tex]
Step 3: To solve for [tex]\( x \)[/tex], divide both sides of the equation by 8.
[tex]\[ x = \frac{38}{8} \][/tex]
Step 4: Simplify the fraction.
[tex]\[ x = \frac{19}{4} \][/tex]
So, the proposed solution is [tex]\( x = \frac{19}{4} \)[/tex].
Step 5: Verify the solution by substituting [tex]\( x = \frac{19}{4} \)[/tex] back into the original equation and check if both sides are equal.
Original equation:
[tex]\[ 4(2x - 4) = 22 \][/tex]
Substitute [tex]\( x = \frac{19}{4} \)[/tex]:
[tex]\[ 4 \left( 2 \cdot \frac{19}{4} - 4 \right) = 22 \][/tex]
[tex]\[ 4 \left( \frac{38}{4} - 4 \right) = 22 \][/tex]
[tex]\[ 4 \left( 9.5 - 4 \right) = 22 \][/tex]
[tex]\[ 4 \times 5.5 = 22 \][/tex]
[tex]\[ 22 = 22 \][/tex]
Since both sides of the equation are equal when [tex]\( x = \frac{19}{4} \)[/tex], the solution is verified.
Therefore, the solution set is:
[tex]\[ \left\{ \frac{19}{4} \right\} \][/tex]
So, the correct choice is:
A. The solution set is [tex]\( \left\{ \frac{19}{4} \right\} \)[/tex].
