To solve the equation [tex]\(-2x + 10 = -4x + 12\)[/tex] for [tex]\(x\)[/tex], let's follow a detailed, step-by-step approach:
1. Move all the terms involving [tex]\(x\)[/tex] to one side of the equation:
Given:
[tex]\[
-2x + 10 = -4x + 12
\][/tex]
To eliminate [tex]\(x\)[/tex] from the right-hand side, add [tex]\(4x\)[/tex] to both sides of the equation:
[tex]\[
-2x + 4x + 10 = -4x + 4x + 12
\][/tex]
Simplifying both sides, we get:
[tex]\[
2x + 10 = 12
\][/tex]
2. Isolate the term involving [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], subtract 10 from both sides of the equation:
[tex]\[
2x + 10 - 10 = 12 - 10
\][/tex]
Simplifying both sides, we get:
[tex]\[
2x = 2
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Now, divide both sides of the equation by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{2x}{2} = \frac{2}{2}
\][/tex]
Simplifying, we obtain:
[tex]\[
x = 1
\][/tex]
Thus, the solution to the equation [tex]\(-2x + 10 = -4x + 12\)[/tex] is:
[tex]\[
x = 1
\][/tex]
