Question
Given that x ∈ R, solve the following inequality and graph the solution on the number line:
-1 ≤ 3 + 4x < 23
-1 ≤ 3 + 4x < 23
✓
Answer
Given : - 1 ≤ 3 + 4x < 23; x ∈ R
⇒ - 1 ≤ 3 + 4x and 3 + 4x < 23
⇒ - 4 ≤ 4x and 4x < 20
$\Rightarrow-\frac{4}{4} \leq x$ and $x<\frac{20}{4}$
⇒ - 1 ≤ x < 5
Solution Set = {x : - 1 ≤ x < 5; x ∈ R}
Solution on the number line is -
⇒ - 1 ≤ 3 + 4x and 3 + 4x < 23
⇒ - 4 ≤ 4x and 4x < 20
$\Rightarrow-\frac{4}{4} \leq x$ and $x<\frac{20}{4}$
⇒ - 1 ≤ x < 5
Solution Set = {x : - 1 ≤ x < 5; x ∈ R}
Solution on the number line is -
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