Question 16 of 40beginner🔧 ApplyNumerical3 marks

Solve the inequality and show the graph of the solution on number line: 5x−3≥3x−55x - 3 \geq 3x - 5

Correct Answer

x ≥\geq -1, i.e., x ∈ [-1, ∞)

Exercise: EXERCISE 5.1 | Q: 18 | (Chapter: Page 7)
For More Understanding

Explanation

This is a linear inequality in one variable. Following the algebraic method shown in the textbook examples (like Example 3 and Example 4), we solve by collecting variable terms on one side and constant terms on the other. The inequality sign direction is preserved since we are dividing by a positive number (2). The solution includes all real numbers greater than or equal to -1, represented using interval notation as [-1, ∞).

Solution Steps

  1. Step 1: We have the inequality: 5x - 3 ≥\geq 3x - 5

  2. Step 2: Subtract 3x from both sides: 5x - 3 - 3x ≥\geq 3x - 5 - 3x, which gives 2x - 3 ≥\geq -5

  3. Step 3: Add 3 to both sides: 2x - 3 + 3 ≥\geq -5 + 3, which gives 2x ≥\geq -2

  4. Step 4: Divide both sides by 2: x ≥\geq -1

  5. Step 5: The solution set is x ∈ [-1, ∞). On the number line, draw a darkened circle at -1 (indicating inclusion) and shade the line to the right towards infinity.

PreviousNext