To solve the equation [tex]\(3x - 7 = 5x + 5\)[/tex], follow these steps:
1. Move all [tex]\(x\)[/tex] terms to one side of the equation:
We want to isolate the variable [tex]\(x\)[/tex] on one side of the equation. To do this, subtract [tex]\(3x\)[/tex] from both sides:
[tex]\[
3x - 7 - 3x = 5x + 5 - 3x
\][/tex]
Simplifying this, we get:
[tex]\[
-7 = 2x + 5
\][/tex]
2. Move the constant terms to the other side:
Next, we need to isolate the term with [tex]\(x\)[/tex] by moving the constants to the other side. Subtract 5 from both sides of the equation:
[tex]\[
-7 - 5 = 2x + 5 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
-12 = 2x
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Now, we need to solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{-12}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x = -6
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that makes the equation [tex]\(3x - 7 = 5x + 5\)[/tex] true is [tex]\(x = -6\)[/tex].
