Question

Solve the inequality and graph its solution. \(-6>x-4\)

Short answer

The solution to the inequality is \(x < -2\). This is graphed as a line with an open dot on -2, with an arrow pointing to the left.

Step-by-step solution

Isolate the x term

Add 4 to both sides of the inequality to isolate \(x\). Doing so, it becomes \(-6+4 > x-4+4\), which simplifies to \(-2 > x\).

Rewrite the inequality

Flip the inequality to read from left to right, where it will read \(x < -2\). This does not affect the inequality as long as the direction of the inequality is also reversed.

Graph the solution

Plot the solution on a number line. Start with a line, place a round, open dot on -2 (indicating that -2 is not included in the solution set). Draw an arrow to the left (indicating all numbers less than -2).