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:
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-3x - 7 ≥ -10
- Add 7: \( -3x ≥ -3 \)
- Divide by -3 (reverse the inequality): \( x ≤ 1 \) (This one matches!)
-
3x + 7 > 10
- Subtract 7: \( 3x > 3 \)
- Divide by 3: \( x > 1 \) (Not a match)
-
3x - 7 < -10
- Add 7: \( 3x < -3 \)
- Divide by 3: \( x < -1 \) (Not a match)
-
-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 \( x \leq 1 \)).