Question 6 of 40beginner🔧 ApplyNumerical2 marks

Solve the inequality for real xx: 3x−7>5x−13x - 7 > 5x - 1

Correct Answer

x ∈ (-∞, -3)

Exercise: EXERCISE 5.1 | Q: 6 | (Page Page 7)
For More Understanding

Explanation

This is a linear inequality problem from Exercise 5.1. Following the method shown in Example 3 of the textbook, we need to isolate x by collecting like terms and then dividing by the coefficient of x. The key rule to remember is that when we multiply or divide both sides of an inequality by a negative number, the inequality sign reverses.

Solution Steps

  1. Step 1: Given inequality: 3x - 7 > 5x - 1

  2. Step 2: Subtract 5x from both sides: 3x - 5x - 7 > -1, which gives -2x - 7 > -1

  3. Step 3: Add 7 to both sides: -2x > 6

  4. Step 4: Divide both sides by -2 (inequality sign reverses): x < -3

  5. Step 5: The solution set is all real numbers less than -3, written as x ∈ (-∞, -3)

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