Question

Solve the inequality and graph its solution. \(-5<4+x \quad\)

Short answer

The solution to the inequality is \( x > -9 \). The graphical representation includes a number line with an open circle at '-9' and a line extending to the right from this point.

Step-by-step solution

Understanding the inequality

Initially we have the inequality \(-5<4+x\). Our goal is to isolate 'x'. To do this, we will subtract '4' from both sides of the inequality.

Isolating the variable 'x'

By subtracting '4' from both sides we get \( -5 - 4 < 4 + x - 4 \). Simplifying this leads to \( -9 < x \). This implies that 'x' is a number greater than '-9'.

Graphing the solution

To graph the solution on a number line, we plot a circle at '-9' and draw a line to the right, indicating that 'x' includes all numbers greater than '-9'. The circle is open because '-9' is not included in the solution set.