QQuestion
Solve the following inequation. Write down the solution set and represent it on the real number line.
− 5(x − 9) ≥ 17 − 9x > x + 2, x ∈ R.
✓Answer
Given:
−5(x − 9) ≥ 17 − 9x > x + 2
First solve −5(x − 9) ≥ 17 − 9x:
⇒ −5x + 45 ≥ 17 − 9x
⇒ −5x + 9x ≥ 17 − 45
⇒ 4x ≥ −28
⇒ x\geq\frac{-28}{4}
⇒ x ≥ −7 … (1)
Now solve 17 − 9x > x + 2:
⇒ 17 − 2 > x + 9x
⇒ 15 > 10x
⇒ 10x < 15
⇒ x < \frac{15}{10}
⇒ x < \frac{3}{2}
x < 1.5 … (2)
Combining (1) and (2):
−7 ≤ x < 1.5
Therefore, the solution set is {x : −7 ≤ x < 1.5}.
On the number line, place a closed point at −7, an open point at 1.5, and shade the interval between them.
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