Sure, let's solve the equation step by step.
The equation we need to solve is:
[tex]\[
-3(x-2) + 4x = 2x - 4
\][/tex]
### Step-by-Step Solution
Step 1: Distribute
First, distribute the [tex]\(-3\)[/tex] across the terms in the parentheses on the left-hand side of the equation.
[tex]\[
-3(x - 2) + 4x = -3x + 6 + 4x = 2x - 4
\][/tex]
Step 2: Combine like terms
Next, combine like terms on the left-hand side of the equation.
[tex]\[
(-3x + 4x) + 6 = 2x - 4
\][/tex]
[tex]\[
x + 6 = 2x - 4
\][/tex]
Step 3: Isolate the variable [tex]\(x\)[/tex]
Move all [tex]\(x\)[/tex] terms to one side and constant terms to the other side. To do this, subtract [tex]\(2x\)[/tex] from both sides.
[tex]\[
x - 2x + 6 = 2x - 2x - 4
\][/tex]
[tex]\[
-x + 6 = -4
\][/tex]
Step 4: Solve for [tex]\(x\)[/tex]
Next, move the constant term from the left side to the right side of the equation by subtracting 6 from both sides.
[tex]\[
-x + 6 - 6 = -4 - 6
\][/tex]
[tex]\[
-x = -10
\][/tex]
Multiply both sides by -1 to solve for [tex]\(x\)[/tex].
[tex]\[
x = 10
\][/tex]
### Check Your Solution
To check if our solution is correct, substitute [tex]\(x = 10\)[/tex] back into the original equation and see if both sides are equal.
Original equation:
[tex]\[
-3(x-2) + 4x = 2x - 4
\][/tex]
Substitute [tex]\(x = 10\)[/tex]:
[tex]\[
-3(10-2) + 4 \cdot 10 = 2 \cdot 10 - 4
\][/tex]
[tex]\[
-3(8) + 40 = 20 - 4
\][/tex]
[tex]\[
-24 + 40 = 16
\][/tex]
[tex]\[
16 = 16
\][/tex]
Since both sides of the equation are equal when [tex]\(x = 10\)[/tex], our solution is confirmed to be correct.
### Conclusion
\#1: We distributed the terms, combined like terms, moved all [tex]\(x\)[/tex] terms to one side and constant terms to the other, and finally solved for [tex]\(x\)[/tex].
\#2: The value of [tex]\(x\)[/tex] that makes the equation true is:
[tex]\[
x = 10
\][/tex]
\#3: Substituting [tex]\(x = 10\)[/tex] back into the original equation confirms that both sides are equal, thereby verifying our solution.
