Sure, let's solve the equation [tex]\( 5(x - 4) = 7x + 5 \)[/tex] step by step.
1. Distribute the 5 on the left side of the equation:
[tex]\[
5(x - 4) = 5 \cdot x - 5 \cdot 4 = 5x - 20
\][/tex]
So the equation can be rewritten as:
[tex]\[
5x - 20 = 7x + 5
\][/tex]
2. Combine like terms by moving all terms involving [tex]\( x \)[/tex] to one side and constant terms to the other side. First, let's move [tex]\( 5x \)[/tex] to the right side by subtracting [tex]\( 5x \)[/tex] from both sides:
[tex]\[
5x - 5x - 20 = 7x - 5x + 5
\][/tex]
This simplifies to:
[tex]\[
-20 = 2x + 5
\][/tex]
3. Next, move the constant term 5 to the left side by subtracting 5 from both sides:
[tex]\[
-20 - 5 = 2x
\][/tex]
Which simplifies to:
[tex]\[
-25 = 2x
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[
\frac{-25}{2} = x
\][/tex]
This gives:
[tex]\[
x = -12.5
\][/tex]
So, the solution to the equation [tex]\( 5(x - 4) = 7x + 5 \)[/tex] is:
[tex]\[
x = -12.5
\][/tex]
