Question

Solve the inequalities for real x : 5x - 8 > 3x + 2.

Answer 1

Concepts of inequality

• Multiplying or dividing by negative to both sides change the inequality sign.
• Solving for one variable: If we are left with a variable with a coefficient 1, that is a solution.
• Sometimes it ends up with a variable with a coefficient 0, then solutions are 'all over reals' or 'no solutions.'

Solving step-by-step

Given inequality for x: $\sf{5x - 8 > 3x + 2}$

→ $\sf{5x - 3x > 2 + 8}$

→ $\sf{2x > 10}$

→ $\sf{x > 5}$

Here we are left with inequality for x with coefficient 1. So, the solution is $\sf{x > 5}$.

Learn more

In the solving method, the terms are transposed. Transposing is a method of changing the side and the sign of a term at the same time.

Transposing the sides shorten the calculation. For example, let's solve the inequality without transposing.

→ $\sf{5x - 8 > 3x + 2}$

→ $\sf{5x - 8 - (3x) > \cancel{3x} + 2 - \cancel{3x}}$

→ $\sf{2x - \cancel{8} + \cancel{8} > 2 + (8)}$

→ $\sf{5x - 3x > 2 + 8}$

→ $\sf{2x > 10}$

→ $\sf{x > 5}$