Bell Work 9/15/17 Solve the Inequalities for x and give two possible solutions. (what are some numbers that would work for x?) 1. 2𝑥≤7 2. 3𝑥−2>9

Inequalities I can… - Represent an inequality in multiple ways. - Interpret the solution sets for inequalities.

Representing an Inequality In words Algebraically On a Number Line Set Notation

Representing With Words *Decide which inequality sign goes with the following phrases* ___ At least ___ Fewer than ___ No less than ___ Not above ___ Does not exceed ___ Over ___ Under ___ Is more than ___ Beneath ___ Minimum ___ Greater than ___ Less than ___ Greater than or equal to ___ Less than or equal to ___ Not equal to ___ More than ___ No more than ___ At most ___ Below ___ Above ___ Not under ___ Smaller than ___ Maximum

Representing Algebraically x is less than 8. x is greater than 8. x is less than or equal to 8. x is greater than or equal to 8. 𝑥<8 𝑥>8 𝑥≤8 𝑥≥8

Represent With a Number Line Change the number line notation to algebraic notation 1. 2. 3. 4.

Representing With Set Notation **Set Notation shows the beginning and ending numbers for an inequality**

Set Notation What do the following sets look like algebraically?

Set Notation 𝑥<8 2. ________ ________ 3. 𝑥 is less than 5 ________ Write the following representations in Set Notation. 𝑥<8 ________ 2. ________ 3. 𝑥 is less than 5 ________

Solutions to Inequalities Things to think about. When you multiply or divide by a negative. When the variables cancel.

Multiply or Divide By A Negative **If you multiply or divide by a negative number, you MUST change the direction of the inequality** Solve the following inequalities for x. −2𝑥≤4 −3𝑥−2>10 −𝑥<−2

What to Do When the Variables Cancel Out If you end with a true statement, the solution is “ALL REAL NUMBERS”. Ex. 5 > 0 If you end with a false statement, there is “NO SOLUTION”. Ex. 10 < 2 2𝑚<2𝑚+3 2𝑚>2𝑚+3 5𝑥+7≥5𝑥−2 2(𝑛+1)≤2𝑛