To determine whether the solution to the equation [tex]\(-5 = -13 + 4x\)[/tex] is [tex]\(x = 2\)[/tex], let's go through each step of the solution process.
1. Begin with the given equation:
[tex]\[
-5 = -13 + 4x
\][/tex]
2. Our goal is to isolate [tex]\(x\)[/tex]. Start by moving [tex]\(-13\)[/tex] to the left side of the equation. To do this, add 13 to both sides:
[tex]\[
-5 + 13 = 4x
\][/tex]
3. Simplify the left side:
[tex]\[
8 = 4x
\][/tex]
4. Now, solve for [tex]\(x\)[/tex] by dividing both sides by 4:
[tex]\[
x = \frac{8}{4}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = 2
\][/tex]
We have found that [tex]\(x = 2\)[/tex].
Now let's check our result by substituting [tex]\(x = 2\)[/tex] back into the original equation to see if both sides are equal.
6. Substitute [tex]\(x\)[/tex] with 2 in the original equation:
[tex]\[
-5 = -13 + 4 \cdot 2
\][/tex]
7. Perform the multiplication:
[tex]\[
-5 = -13 + 8
\][/tex]
8. Simplify the right side:
[tex]\[
-5 = -5
\][/tex]
Since both sides of the equation are equal, the solution [tex]\(x = 2\)[/tex] is correct. Therefore, the statement [tex]\(x = 2\)[/tex] solves the equation [tex]\(-5 = -13 + 4x\)[/tex] is True.
