Question

which of the following is a solution to the inequality below?
$7 < 11 - \frac{g}{14}$
$g = 28$
$g = 70$
$g = 84$
$g = 112$
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Explanation:

Step1: Isolate the variable term

Subtract 11 from both sides:
$2 - 11 < 11 - \frac{g}{14} - 11$
$-9 < -\frac{g}{14}$

Step2: Eliminate negative coefficient

Multiply both sides by -14 (reverse inequality):
$(-9) \times (-14) > g$
$126 > g$

Step3: Test each option

Check if $g < 126$:

• $g=28$: $28 < 126$ → True
• $g=70$: $70 < 126$ → True
• $g=84$: $84 < 126$ → True
• $g=112$: $112 < 126$ → True

Verify in original inequality for confirmation:
For $g=28$: $2 < 11 - \frac{28}{14} = 11-2=9$ → $2<9$ True
For $g=70$: $2 < 11 - \frac{70}{14}=11-5=6$ → $2<6$ True
For $g=84$: $2 < 11 - \frac{84}{14}=11-6=5$ → $2<5$ True
For $g=112$: $2 < 11 - \frac{112}{14}=11-8=3$ → $2<3$ True

Answer:

All options are solutions:
A. $g = 28$
B. $g = 70$
C. $g = 84$
D. $g = 112$