X on a Number Line

Concept

Solve an inequality to find the value of x on the number line.

Rules

1. Use the properties of inequalities to isolate the variable on one side of the inequality.
2. Simplify the other side of the inequality.
3. If the inequality is < or >, put an open circle on the number line at the indicated value. If the inequality is ≤ or ≥, put a filled circle on the number line at the indicated value.
4. Draw a ray in the appropriate direction indicated by the inequality symbol. If < or ≤, then arrow goes to the left, if > or ≥, then arrow goes to the right.

Example

Solve the inequality and graph the solution.
$\fn_phv 6-8x> 22$

Solution

$\fn_phv 6-8x> 22$
$\fn_phv 6-8x-6> 22-6$
$\fn_phv -8x> 16$
$\fn_phv \frac{-8x}{-8}< \frac{16}{-8}$
$\fn_phv x< -2$

$\fn_phv {\color{Red} x<-2}$ indicates all values less than $\fn_phv {\color{Red} -2}$ .

Practice X on a Number Line

Practice Problem 1

Solve the inequality and graph the solution.
$\fn_phv 3+x\leq -4$

Practice Problem 2

Solve the inequality and graph the solution.
$\fn_phv \frac{x}{8}> -\frac{3}{5}$

Practice Problem 3

Which of the solutions makes the inequality true?
$\fn_phv 5x-2\geq 18$

Practice Problem 4

Alison is x years old. Her brother Tom is 3 times as old as Alison was 4 years ago. Tom has no more than 29 years old.
Select the correct inequality that represents the solution.