Solve the inequality. 2(4x - 3) ≥ -3(3x) + 5x

Solution:

Given:

A linear inequality 2(4x - 3) ≥ - 3(3x) + 5x

Rearrange the terms on LHS

2 (4x - 3) + 3 (3x) - 5x ≥ 0

Simplifying the terms, we get

2 (4x - 3) + 9x - 5x ≥ 0

Using the multiplicative distributive property

8x - 6 + 9x - 5x ≥ 0

Rearranging the equation

8x + 9x - 5x ≥ 6

12x ≥ 6

Divide both sides by 6

2x ≥ 1

x ≥ 1/2

Therefore, x ≥ 1/2.

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Solve the inequality. 2(4x - 3) ≥ -3(3x) + 5x?

Summary:

Solving the inequality 2(4x - 3) ≥ -3(3x) + 5x we get x ≥ 1/2.