Sure! Let's solve the given linear equation step by step.
The original equation is:
[tex]$2x + 9(x - 1) = 8(2x + 2) - 5$[/tex]
Step 1: Apply the distributive property.
On the left side:
[tex]$2x + 9(x - 1) = 2x + 9x - 9 = 11x - 9$[/tex]
On the right side:
[tex]$8(2x + 2) - 5 = 8 \cdot 2x + 8 \cdot 2 - 5 = 16x + 16 - 5 = 16x + 11$[/tex]
So the equation simplifies to:
[tex]$11x - 9 = 16x + 11$[/tex]
Step 2: Combine like terms on each side.
On the left side, the terms are already combined as [tex]\(11x - 9\)[/tex].
On the right side, the terms are already combined as [tex]\(16x + 11\)[/tex].
So we have:
[tex]$11x - 9 = 16x + 11$[/tex]
Step 3: Use the subtraction property of equality to isolate the variable term.
Subtract [tex]\(11x\)[/tex] from both sides:
[tex]$11x - 9 - 11x = 16x + 11 - 11x$[/tex]
This simplifies to:
[tex]$-9 = 5x + 11$[/tex]
Next, subtract [tex]\(11\)[/tex] from both sides to isolate the constant:
[tex]$-9 - 11 = 5x + 11 - 11$[/tex]
This simplifies to:
[tex]$-20 = 5x$[/tex]
Step 4: Use the division property of equality to solve for [tex]\(x\)[/tex].
Divide both sides by [tex]\(5\)[/tex]:
[tex]$\frac{-20}{5} = x$[/tex]
This simplifies to:
[tex]$-4 = x$[/tex]
So, the solution to the equation is:
[tex]$x = -4.$[/tex]
