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Chapter 12: Problem 259

Find the solution set of inequality \(5 \mathrm{x}-9>2 \mathrm{x}+3\).

Short Answer

Expert verified
The solution set of the inequality \(5x - 9 > 2x + 3\) is \(x > 4\).

Step by step solution

01

Subtract 2x from both sides of the inequality

Subtract 2x from both sides to isolate x terms on one side and constants on the other side. \(5x - 9 - 2x > 2x + 3 - 2x\) Simplify the inequality: \(3x - 9 > 3\)
02

Add 9 to both sides of the inequality

Add 9 to both sides to isolate the x term on the left side and constants on the right side. \(3x - 9 + 9 > 3 + 9\) Simplify the inequality: \(3x > 12\)
03

Divide both sides of the inequality by the coefficient of x

Divide both sides by 3 to solve for x. \(\frac{3x}{3} > \frac{12}{3}\) Simplify the inequality: \(x > 4\) The solution set of the inequality \(5x - 9 > 2x + 3\) is \(x > 4\).

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