Question 5 of 40beginner🔧 ApplyNumerical2 marks

Solve the inequality for real xx: 4x+3<5x+74x + 3 < 5x + 7

Correct Answer

x > -4, Solution set: (-4, ∞)

Exercise: EXERCISE 5.1 | Q: 5 | (Page Page 7)
For More Understanding

Explanation

This question follows the same pattern as Example 3 and Example 5 from the textbook. The student needs to collect like terms and solve for x. The key step is isolating x on one side of the inequality. When dividing or multiplying by a negative number, the inequality sign reverses, but in this case, we get a positive coefficient for x, so the sign remains unchanged.

Solution Steps

  1. Step 1: Given inequality: 4x + 3 < 5x + 7

  2. Step 2: Subtracting 4x from both sides: 3 < x + 7

  3. Step 3: Subtracting 7 from both sides: 3 - 7 < x, which gives -4 < x

  4. Step 4: This can be written as x > -4

  5. Step 5: The solution set is (-4, ∞), i.e., all real numbers greater than -4

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