Solve the inequality 3x + 5 < x − 7, represent the solution on the number line and express it in set-builder form.
▶ Show Detailed Solution
3x + 5 < x − 7 ⇒ 3x − x < −7 − 5 ⇒ 2x < −12 ⇒ x < −6. Solution: x ∈ (−∞, −6), i.e. {x : x ∈ R, x < −6}. Number line: open circle at −6, arrow to the left.
📅 Year 2023
Q1
CBSE Board Exam 20234 Marks
Solve the system of inequalities 3x − 7 > 2(x − 6) and 6 − x > 11 − 2x, and represent the solution set on the number line.
▶ Show Detailed Solution
First: 3x − 7 > 2x − 12 ⇒ x > −5. Second: 6 − x > 11 − 2x ⇒ 2x − x > 11 − 6 ⇒ x > 5. Intersection: x > 5. Solution set: {x : x > 5}, open circle at 5, arrow to the right.