Question
Solve the following inequalities and represent the solution set on a number line:
$0<\frac{3 x-2}{4} \leq 2$
$0<\frac{3 x-2}{4} \leq 2$
✓
Answer
The given inequality is$0<\frac{3 x-2}{4} \leq 2$
Which is equivalent to
0 < 3x - 2 ≤ 8
⇒ 2 < 3x ≤ 8 + 2
⇒ 2 < 3x ≤ 10
⇒ 2/3 < x ≤ 10/3
The graph of this set is 2/3 < x ≤ 10/3.
Which is equivalent to
0 < 3x - 2 ≤ 8
⇒ 2 < 3x ≤ 8 + 2
⇒ 2 < 3x ≤ 10
⇒ 2/3 < x ≤ 10/3
The graph of this set is 2/3 < x ≤ 10/3.
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