Question

What is the solution for the inequality below? 3(2x–1)<2(4+3x)

a) x<1
b) x>1
c) x<−1
d) x>−1

Answer 1

To solve the inequality 3(2x–1) < 2(4+3x), distribute, simplify, and isolate the variable x by subtracting 6x from both sides. As -3 is always less than 8, the solution is the entire number line. Thus, the solution is x>-1.

Step-by-step explanation:

To solve the inequality 3(2x–1) < 2(4+3x), we need to simplify and isolate the variable x. Here are the steps:

1. Distribute on both sides: 6x - 3 < 8 + 6x
2. Subtract 6x from both sides to get rid of the variable terms: -3 < 8
3. Since this inequality is always true (-3 is always less than 8), the solution is the entire number line. Thus, x can be any real number.

Therefore, the correct answer is d) x>-1.