Let's solve the equation [tex]\( (x - 1) = 2x + 5 \)[/tex] step-by-step:
1. Starting Equation:
[tex]\[
x - 1 = 2x + 5
\][/tex]
2. Isolate the [tex]\(x\)[/tex] term: We want to get all [tex]\(x\)[/tex]-terms on one side, thus we subtract [tex]\(2x\)[/tex] from both sides of the equation:
[tex]\[
x - 1 - 2x = 5
\][/tex]
Simplify the left side:
[tex]\[
-x - 1 = 5
\][/tex]
3. Isolate the constant term: We add 1 to both sides to move the constant term to the right side:
[tex]\[
-x - 1 + 1 = 5 + 1
\][/tex]
Simplify both sides:
[tex]\[
-x = 6
\][/tex]
4. Solve for [tex]\(x\)[/tex]: Finally, we multiply both sides by [tex]\(-1\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[
x = -6
\][/tex]
Thus, the solution to the equation [tex]\( (x - 1) = 2x + 5 \)[/tex] is:
[tex]\[
x = -6
\][/tex]
