To solve the given equation, let's go through it step-by-step:
[tex]\[ 4x + 8(x - 10) = 4(x + 8) \][/tex]
1. Distribute the constants inside the parentheses on both sides of the equation:
[tex]\[ 4x + 8x - 80 = 4x + 32 \][/tex]
2. Combine like terms on the left-hand side:
[tex]\[ 12x - 80 = 4x + 32 \][/tex]
3. Move all terms involving [tex]\( x \)[/tex] to one side by subtracting [tex]\( 4x \)[/tex] from both sides:
[tex]\[ 12x - 4x - 80 = 32 \][/tex]
[tex]\[ 8x - 80 = 32 \][/tex]
4. Isolate the variable term [tex]\( 8x \)[/tex] by adding 80 to both sides:
[tex]\[ 8x = 112 \][/tex]
5. Solve for [tex]\( x \ ) by dividing both sides by 8:
\[ x = 14 \]
So the solution to the equation \( 4x + 8(x - 10) = 4(x + 8) \)[/tex] is [tex]\( x = 14 \)[/tex].
Therefore, [tex]\( x = 14 \)[/tex].
