Solve x−13≤12

Question

𝑥
−
1
3
≤
1
2
. (1 point)
Responses

x≥16
𝑥
≥
1
6
x greater-than-or-equal-to Start Fraction 1 over 6 End Fraction

x≤16
𝑥
≤
1
6
x less-than-or-equal-to Start Fraction 1 over 6 End Fraction

x≥56
𝑥
≥
5
6
x greater-than-or-equal-to Start Fraction 5 over 6 End Fraction

x≤56....

Answer 1

To solve the inequalities:

1. First inequality: \( x - 13 \leq 12 \)

   We solve this step by step:

   \[ x - 13 \leq 12 \]

   Add 13 to both sides:

   \[ x \leq 12 + 13 \]

   \[ x \leq 25 \]

2. Second inequality: \( \frac{x}{3} \leq \frac{1}{2} \)

   Multiply both sides by 3 (since 3 is positive, the inequality stays the same):

   \[ x \leq \frac{1}{2} \cdot 3 \]

   \[ x \leq \frac{3}{2} \]

So, we have the two inequalities:

• \( x \leq 25 \)
• \( x \leq \frac{3}{2} \)

The more restrictive condition is \( x \leq \frac{3}{2} \) (which is \( 1.5 \)).

Thus, combining both inequalities results in:

\[ x \leq \frac{3}{2} \]

Therefore, the solution to the system of inequalities is:

Response: \( x \leq \frac{3}{2} \)

This corresponds to the option nearest to \( x \leq \frac{1}{6} \) (which is incorrect) and subsequently aligns with your solution criteria.

The valid choice is:

\( x \leq \frac{3}{2} \).