Question

On solving the inequality 2x – 3< x + 1 ≤ 4x+7, we get -2 ≤ x <4.

A. True
B. False
Show your work to support your answer

Answer 1

To solve the inequality 2x - 3 < x + 1 ≤ 4x + 7, we need to break it down into two separate inequalities. First, solve the inequality 2x - 3 < x + 1. Then, solve the inequality x + 1 ≤ 4x + 7. Finally, combine the two inequalities to find the solution.

Step-by-step explanation:

To solve the inequality 2x – 3 < x + 1 ≤ 4x + 7, we need to break it down into two separate inequalities.

1. First, solve the inequality 2x - 3 < x + 1:

• Add 3 to both sides: 2x < x + 4
• Subtract x from both sides: x < 4

Next, solve the inequality x + 1 ≤ 4x + 7:

• Subtract x from both sides: 1 ≤ 3x + 7
• Subtract 7 from both sides: -6 ≤ 3x
• Divide by 3: -2 ≤ x

Combining the two inequalities, we have -2 ≤ x < 4. Therefore, the statement 'True' is correct.