Let's carefully examine the steps provided to identify where the error occurs.
### Line (1) to Line (2):
Line (1): [tex]\(-2(-5x + 4) \geq -10\)[/tex]
First, distribute [tex]\(-2\)[/tex] on the left-hand side:
[tex]\[
-2 \cdot -5x + (-2) \cdot 4 \geq -10
\][/tex]
This simplifies to:
[tex]\[
10x - 8 \geq -10
\][/tex]
Adding 8 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
10x \geq -10 + 8
\][/tex]
[tex]\[
10x \geq -2
\][/tex]
Dividing both sides by 10:
[tex]\[
x \geq -\frac{2}{10}
\][/tex]
[tex]\[
x \geq -\frac{1}{5}
\][/tex]
Therefore, we see that the expression [tex]\(-5x + 4 \geq 5\)[/tex] in Line (2) isn't correct based on the steps we showed. Line (1) to Line (2) is the point where the error occurred.
### Verification of other steps:
Let's still go through Line (2) to Line (3) for completion:
Line (2): [tex]\(-5x + 4 \geq 5\)[/tex]
Subtract 4 from both sides:
[tex]\[
-5x \geq 1
\][/tex]
This step is correct. No error here.
Line (3) to Line (4):
Line (3): [tex]\(-5x \geq 1\)[/tex]
Divide both sides by [tex]\(-5\)[/tex]. Remember to flip the inequality sign when dividing by a negative number:
[tex]\[
x \leq -\frac{1}{5}
\][/tex]
This step is also correct.
Since in Line (5), no further steps are shown, there are no errors to analyze beyond Line (4).
### Answer:
The error occurred from Line (1) to Line (2).
