Question

Which inequality represents the graph below

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 w/ a dot on 1 and the arrow pointing backwards to -10
(1 point)
○ -3x - 7 ≥ -10
○ 3x + 7 > 10
○ 3x - 7 < -10
○ -3x + 7 < 10

Answer 1

To determine which inequality corresponds to the graph you described (with a dot at 1 and an arrow pointing back towards -10), we need to recognize that the graph indicates that values less than or equal to 1 are included in the solution.

This situation typically corresponds to an inequality of the form \( x \leq 1 \) or similar, depending on how x is expressed. Analyzing the options provided, let’s rewrite the inequalities to isolate x:

1. **-3x - 7 ≥ -10**
- Add 7: \( -3x ≥ -3 \)
- Divide by -3 (reverse the inequality): \( x ≤ 1 \) (This one matches!)

2. **3x + 7 > 10**
- Subtract 7: \( 3x > 3 \)
- Divide by 3: \( x > 1 \) (Not a match)

3. **3x - 7 < -10**
- Add 7: \( 3x < -3 \)
- Divide by 3: \( x < -1 \) (Not a match)

4. **-3x + 7 < 10**
- Subtract 7: \( -3x < 3 \)
- Divide by -3 (reverse the inequality): \( x > -1 \) (Not a match)

The inequality that matches the graph you described is:
**-3x - 7 ≥ -10** (This means \( x \leq 1 \)).