Let's solve the equation step-by-step:
[tex]\[ 2(x+2) - 3(5 - x) = x + 5(x - 3) \][/tex]
Step 1: Distribute the constants on both sides of the equation.
[tex]\[ 2(x + 2) = 2 \cdot x + 2 \cdot 2 = 2x + 4 \][/tex]
[tex]\[ -3(5 - x) = -3 \cdot 5 + 3 \cdot x = -15 + 3x \][/tex]
[tex]\[ x + 5(x - 3) = x + 5 \cdot x - 5 \cdot 3 = x + 5x - 15 = 6x - 15 \][/tex]
So, the equation now looks like:
[tex]\[ 2x + 4 - 15 + 3x = 6x - 15 \][/tex]
Step 2: Combine like terms on the left-hand side.
[tex]\[ 2x + 3x + 4 - 15 = 5x - 11 \][/tex]
So the equation simplifies to:
[tex]\[ 5x - 11 = 6x - 15 \][/tex]
Step 3: Isolate [tex]\( x \)[/tex] by moving all terms involving [tex]\( x \)[/tex] to one side and constants to the other side.
First, subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[ -11 = x - 15 \][/tex]
Then, add 15 to both sides:
[tex]\[ -11 + 15 = x \][/tex]
[tex]\[ 4 = x \][/tex]
Therefore, the solution to the equation is:
[tex]\[ x = 4 \][/tex]
