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Chapter 6: Problem 38

Solve each inequality and graph the solution set on a number line. \(3 x-8<2 x+11\)

Short Answer

Expert verified
The solution to the inequality \(3 x-8<2 x+11\) is \(x < 19\).

Step by step solution

01

- Move All Terms Involving x to One Side

To start, subtract \(2x\) from both sides of the inequality, obtaining: \(3x - 2x < 2x - 2x + 11)~ which simplifies to ~ x - 8 < 11.
02

- Fully Isolate x

Next, add 8 on both sides of the inequality, obtaining: \(x - 8 + 8 < 11 + 8\) which simplifies to \(x < 19\).
03

- Graph the Solution

The solution \(x < 19\) represents all numbers less than 19. On a number line, this is represented by an open circle at 19 (since 19 is not included in the solution) with an arrow pointing to the left.

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