Question 20 of 40intermediate🔧 ApplyNumerical3 marks

Solve the inequality and show the graph of the solution on number line: x2≥(5x−2)3−(7x−3)5\frac{x}{2} \geq \frac{(5x - 2)}{3} - \frac{(7x - 3)}{5}

Correct Answer

x ≥\geq -2/7, Solution set: [-2/7, ∞)

Exercise: EXERCISE 5.1 | Q: 20 | (Page Page 7)
For More Understanding

Explanation

This question involves solving a linear inequality with fractions. Following the pattern from Example 6 in the textbook, we first combine the fractions on the right-hand side by taking LCM, then cross-multiply to eliminate denominators, and finally solve for x. The key steps involve finding LCM of 3 and 5 (which is 15), simplifying, and then cross-multiplying with the LCM of 2 and 15 (which is 30). The solution requires careful handling of signs and inequality rules.

Solution Steps

  1. Step 1: We have x/2 ≥\geq (5x-2)/3 - (7x-3)/5. Taking LCM of 3 and 5 on RHS (LCM = 15): x/2 ≥\geq 5(5x-2)/15 - 3(7x-3)/15

  2. Step 2: Simplify the RHS: x/2 ≥\geq (25x-10-21x+9)/15 = (4x-1)/15

  3. Step 3: Cross multiply (multiply both sides by 30, LCM of 2 and 15): 15x ≥\geq 2(4x-1)

  4. Step 4: Simplify: 15x ≥\geq 8x - 2, or 15x - 8x ≥\geq -2, or 7x ≥\geq -2

  5. Step 5: Divide by 7: x ≥\geq -2/7. Solution set is [-2/7, ∞)

  6. Step 6: Graphical representation: On number line, draw a dark line from -2/7 extending right towards ∞ with a filled circle at -2/7 (indicating inclusion).

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