Question

Question content area left
Part 1
Solve using the addition and multiplication principles.
3xminus5less than or equalsnbsp 7
.
.
.
Question content area right
Part 1
Select the correct choice below and fill in the answer box within your choice.
​(Simplify your​ answer.)
A.
The solution set is​ {x | xgreater than or equals
  
enter your response here​}.
B.
The solution set is​ {x | xless than or equals
  
enter your response here​}.
C.
The solution set is​ {x | xgreater than
  
enter your response here​}.
D.
The solution set is​ {x | xless than
  
enter your response here​}.

Answer 1

To solve the inequality \( 3x - 5 \leq 7 \), we will use the addition and multiplication principles.

1. **Add 5 to both sides:**

\[
3x - 5 + 5 \leq 7 + 5
\]

This simplifies to:

\[
3x \leq 12
\]

2. **Divide both sides by 3:**

\[
\frac{3x}{3} \leq \frac{12}{3}
\]

This simplifies to:

\[
x \leq 4
\]

The solution set can be expressed in set-builder notation. Thus, the correct choice is:

**B. The solution set is** {x | x ≤ 4}.

So the answer to fill in the box would be **4**.