Let's solve the given equation step by step.
Given equation:
[tex]\[ 2(5x + 8) = 6x + 20 \][/tex]
Step 1: Distribute the 2 on the left side of the equation.
[tex]\[ 2 \cdot (5x + 8) = 2 \cdot 5x + 2 \cdot 8 \][/tex]
[tex]\[ 10x + 16 \][/tex]
So the equation now is:
[tex]\[ 10x + 16 = 6x + 20 \][/tex]
Step 2: Subtract [tex]\( 6x \)[/tex] from both sides of the equation to get the terms involving [tex]\( x \)[/tex] on one side.
[tex]\[ 10x + 16 - 6x = 20 \][/tex]
[tex]\[ 4x + 16 = 20 \][/tex]
Step 3: Subtract 16 from both sides of the equation to isolate the term with [tex]\( x \)[/tex] on one side.
[tex]\[ 4x + 16 - 16 = 20 - 16 \][/tex]
[tex]\[ 4x = 4 \][/tex]
Step 4: Divide both sides of the equation by 4 to solve for [tex]\( x \)[/tex].
[tex]\[ \frac{4x}{4} = \frac{4}{4} \][/tex]
[tex]\[ x = 1 \][/tex]
So, the solution to the equation [tex]\( 2(5x + 8) = 6x + 20 \)[/tex] is:
[tex]\[ x = 1 \][/tex]
Thus, the correct answer is:
C. [tex]\( x = 1 \)[/tex]
