To determine which equation is equivalent to the given equation [tex]\(-4(x - 5) + 8x = 9x - 3\)[/tex], let's solve it step by step.
First, we simplify the left-hand side:
[tex]\[
-4(x - 5) + 8x
\][/tex]
Distribute the [tex]\(-4\)[/tex]:
[tex]\[
-4x + 20 + 8x
\][/tex]
Combine like terms:
[tex]\[
4x + 20
\][/tex]
So the left-hand side becomes [tex]\(4x + 20\)[/tex]. Now let's equate this to the right-hand side:
[tex]\[
4x + 20 = 9x - 3
\][/tex]
Next, we isolate the variable [tex]\(x\)[/tex] by moving all terms involving [tex]\(x\)[/tex] to one side and constants to the other:
Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[
20 = 5x - 3
\][/tex]
Add 3 to both sides:
[tex]\[
23 = 5x
\][/tex]
Divide by 5:
[tex]\[
x = \frac{23}{5}
\][/tex]
Now let's re-examine the multiple choices. The equivalent form of this equation that we found should show a clear relation between [tex]\(x\)[/tex] and a constant. If we rearrange the final isolated term [tex]\(5x = 23\)[/tex] to match one of the provided options correctly, we see that it simplifies to:
[tex]\[
5x = 23
\][/tex]
The correct form [tex]\(5x = 23\)[/tex] corresponds directly to none of the provided options.
Thus, the equivalent equation provided in the multiple choices must focus on rearranging the aspects of the equation differently:
### Review of the given choices:
A. [tex]\(-5x = 2\)[/tex] - This does not match.
B. [tex]\(-5x = -23\)[/tex] - This is the negative equivalent.
C. [tex]\(5x = 17\)[/tex] - [tex]\(5x = 23\)[/tex] is directly not equal.
D. [tex]\(5x = -12\)[/tex] - This does directly not equal 23.
Interpreting correctly about [tex]\(-5x\)[/tex] equivalent form of the identified values:
Given result confirms:
### Correct validated equation,
B. [tex]\(-5x = -23\)[/tex]
It has shown like [tex]\(23 -5x = 0 -> 5x = 23 exactly same .
Therefore, equivalent choice is:
Answer: B. \(-5x = -23\)[/tex]
