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Chapter 6: Problem 37

Solve each inequality and graph the solution set on a number line. \(5 x-9<4 x+7\)

Short Answer

Expert verified
The solution to the inequality is \(x < 16\). It can be graphed on a number line with a line extending from 16 to the left, indicating all numbers less than 16.

Step by step solution

01

Simplify the Inequality

Subtract \(4x\) from both sides of the inequality to isolate the variable terms on one side. This results in \(5x - 4x < 9 + 7.\)
02

Solve for x

Simplify both sides of the equation to get \(x < 16.\)
03

Graph the Solution

On a number line, plot a circle at 16 to represent that 16 is not included in the solution set. Draw a line to the left of 16, demonstrating that all values less than 16 are included in the solution set.

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