To solve for [tex]\(x\)[/tex] in the equation [tex]\(13x - 6 = 8x + 19\)[/tex], follow these steps:
1. Isolate the variable terms on one side of the equation.
We want to get all the [tex]\(x\)[/tex] terms on one side and the constants on the other. To do this, subtract [tex]\(8x\)[/tex] from both sides of the equation:
[tex]\[
13x - 8x - 6 = 8x - 8x + 19
\][/tex]
Simplifying this, we get:
[tex]\[
(13x - 8x) - 6 = 19
\][/tex]
[tex]\[
5x - 6 = 19
\][/tex]
2. Isolate the constant term on the other side of the equation.
To remove the -6 from the left side, add 6 to both sides of the equation:
[tex]\[
5x - 6 + 6 = 19 + 6
\][/tex]
Simplifying this, we get:
[tex]\[
5x = 25
\][/tex]
3. Solve for the variable [tex]\(x\)[/tex].
To isolate [tex]\(x\)[/tex], divide both sides of the equation by 5:
[tex]\[
\frac{5x}{5} = \frac{25}{5}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 5
\][/tex]
Thus, the solution to the equation [tex]\(13x - 6 = 8x + 19\)[/tex] is:
[tex]\[
x = 5
\][/tex]
