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Jordan solved the equation [tex]-7x + 25 = 48[/tex]; his work is shown below. Identify the error and where it was made.

Step 1: [tex]\[ -7x + 25 - 25 = 48 - 25 \][/tex]
Step 2: [tex]\[ -7x = 23 \][/tex]
Step 3: [tex]\[ \frac{-7x}{7} = \frac{23}{7} \][/tex]
Step 4: [tex]\[ x = \frac{23}{7} \][/tex]

A. Step 1: He should have added 25 to each side.
B. Step 1: He should have divided both sides by -7.
C. Step 3: He should have divided both sides by -7.
D. Step 3: He should have multiplied both sides by -7.

Sagot :

GinnyAnsweridn
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.
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