Question 8 of 40beginner🔧 ApplyNumerical2 marks

Solve the inequality for real xx: 3(2−x)≥2(1−x)3(2 - x) \geq 2(1 - x)

Correct Answer

We have, 3(2−x)≥2(1−x)3(2 - x) \geq 2(1 - x) or 6−3x≥2−2x6 - 3x \geq 2 - 2x or −3x+2x≥2−6-3x + 2x \geq 2 - 6 (Rule 1) or −x≥−4-x \geq -4 or x≤4x \leq 4 (Rule 2)

The solutions of the inequality are given by x≤4x \leq 4, i.e., all real numbers xx which are less than or equal to 4. Therefore, the solution set of the inequality is x∈(−∞,4]x \in (-\infty, 4].

Exercise: EXERCISE 5.1 | Q: 8 | (Page Page 7)
For More Understanding

Explanation

The solution follows the standard procedure for linear inequalities outlined in the provided examples. First, the brackets are expanded. Then, Rule 1 is applied to group the variable terms on one side and constant terms on the other. Finally, Rule 2 is applied when dividing by a negative number (-1), which reverses the inequality sign from ≥\geq to ≤\leq. The solution set is expressed in interval notation as (−∞,4](-\infty, 4].

Solution Steps

  1. Step 1: Expand the expression to get 6−3x≥2−2x6 - 3x \geq 2 - 2x.

  2. Step 2: Rearrange terms using Rule 1 to get −x≥−4-x \geq -4.

  3. Step 3: Divide by -1 using Rule 2 (reversing sign) to get x≤4x \leq 4.

  4. Step 4: Write the solution set as (−∞,4](-\infty, 4].

PreviousNext