Children under 12 can enter the museum at no charge. Write the inequality x < 12 If you are 12 can you get in free? no If you are 11 can you get in free? yes If you are 5 can you get in free? yes

< < < > < > < <

An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to

x ≥ 7 All numbers greater than 7 (including 7)

≥ m 1.Draw “the river” to separate the inequality into 2 sides 2.Add 3 to both sides 3.Simplify vertically 4.Put the variable on the left hand side m ≤ 10 All numbers less than 10 (including 10)

x + 2 > x > -1 1.Draw “the river” to separate the inequality into 2 sides 2.Eliminate the double sign 3.Subtract 2 from both sides 4.Simplify vertically All numbers greater than -1

More Examples 10x > x > -2 All numbers greater than -2 make this problem true!

-5 -5 t ≥ -4 t ≤ -4 1.Draw “the river” to separate the inequality into 2 sides 2.Divide both sides by -5 3.Reverse your inequality sign! All numbers less than -4 (including -4)

1.Draw “the river” to separate the inequality into 2 sides 2.Multiply each side by Reverse your inequality sign! All numbers greater than -8