To solve the given equation [tex]\(-7x + 25 = 48\)[/tex], let's go through Jordan's steps and identify where his error occurred step-by-step.
### Original Equation:
[tex]\(-7x + 25 = 48\)[/tex]
### Step 1: Subtraction
Jordan subtracted 25 from both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
-7x + 25 - 25 = 48 - 25
\][/tex]
This simplifies to:
[tex]\[
-7x = 23
\][/tex]
Step 1 is correct.
### Step 2: Simplification
The equation after the subtraction step is:
[tex]\[
-7x = 23
\][/tex]
Step 2 is simply rewriting the equation after the subtraction, so it is also correct.
### Step 3: Division
In Step 3, Jordan attempted to isolate [tex]\(x\)[/tex] by dividing both sides of the equation by 7. His work showed:
[tex]\[
\frac{-7x}{7} = \frac{23}{7}
\][/tex]
However, Jordan made a mistake here. To correctly isolate [tex]\(x\)[/tex], he should have divided both sides by [tex]\(-7\)[/tex], not 7. The correct operation should be:
[tex]\[
\frac{-7x}{-7} = \frac{23}{-7}
\][/tex]
This simplifies to:
[tex]\[
x = -\frac{23}{7}
\][/tex]
Therefore, the error occurred in Step 3. Jordan should have divided both sides by [tex]\(-7\)[/tex] instead of 7.
### Step 4: Incorrect Result from Step 3
Jordan’s incorrect division in Step 3 led to an incorrect expression for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{23}{7}
\][/tex]
### Conclusion:
The correct answer to the question is:
c Step 3: He should have divided both sides by -7.
