Question

Solve the inequality and graph its solution. \(-3>2 x-5\)

Short answer

The solution to the inequality \(-3 > 2x - 5\) is \(x < 1\). This is represented on a number line with an open circle at 1 and an arrow pointing left, indicating values less than 1.

Step-by-step solution

Addition/subtraction

First, the constant from the right hand side must be moved to the left hand side of the inequality. This can be done by adding 5 to both sides. So, the inequality -3 > 2x - 5 becomes (-3+5) > 2x, simplifying to 2 > 2x.

Division

Divide each side by 2 (the coefficient of x) to isolate x: \(2/2 > 2x/2\). This results in 1 > x.

Swap sides

Normally, we write this with 'x' on the left hand side: x < 1.

Graph the solution

To graph the solution, draw a number line. The solution x < 1 indicates that x can be any number less than 1. On the number line, a open circle (because x cannot equal to 1) is placed at 1, and an arrow is drawn pointing towards the left to denote 'less than'.