Summer Assignment Review

Graphing Compound InequalitiesAnd Absolute Value Inequalities

Compound Inequalities

AND compound inequalities should create a range of values.

falls between -2 and 3 on the number line.

Don’t assume that the given inequality creates this range.

can not be both to the left of -2 and to the right of 3 on the number line . There is no solution.

Compound Inequalities

OR compound inequalities should create two ranges of values.

is either to the left of -2 or to the right of 3 on the number line.

AND compound inequalities should create a range of values.

can be anywhere on the number line. The solution is All Real Numbers.

PracticeGraph each compound inequality.

1)

2)

3)

4)

5)

−3<𝑥<4

𝑥<−4𝑜𝑟 𝑥 ≥2

𝑥>−1𝑎𝑛𝑑 𝑥≤5

𝑥≥−3𝑜𝑟 𝑥<3

𝑥≤0𝑎𝑛𝑑 𝑥 ≥3

All Real Numbers

No Solutions

Absolute Value InequalitiesWhen we say that , we are saying that the distance between x and 0 is 3.

When we say that , we are saying that the distance between x and 0 is less than 3.

When we say that , we are saying that the distance between x and 0 is greater than 3.

The inequalities < and ≤ lead to “and” relationships

The inequalities > and lead to “or” relationships

−3<𝑥<3

𝑥<−3𝑂𝑅𝑥>3

Solving Absolute Value Inequalities

Case 2 - modified method: Drop the absolute value bars, flip the inequality symbol and change the sign of the term on the right. 2 𝑥−1<−7

2 𝑥<−6𝑥<−3

Solve and Graph an Abs. Val. Ineq.Example : Solve Graph your solution.

Step 1: Is it and or or?

For the second, flip the inequality andchange the sign of the 7

Step 2: Solve both

Step 3: Graph

This is ≥ so it is “or”. Set up two inequalities.

|𝑥−5|≥7

𝑥−5≥7 𝑥−5≤−7

𝑥≥12 𝑥≤−2

or 𝑥≤−2

-3 -2 -1 · · · 11 12 13

Solve and Graph an Abs. Val. Ineq.Example : Solve Graph your solution.

Step 1: Is it and or or?

Step 2: Solve +5 +5 +5

-4 -4 -4Step 3: Graph

We don’t know yet, get the abs. val. alone.

|−4 𝑥−5|+3<9

|−4 𝑥−5|<6Now : It is < , so it is an “and” inequality. Drop the abs. val. Bars and put -6 < on the left.

Practice

𝑥>5𝑜𝑟 𝑥<−11 −5<𝑤<6 −0.2≤𝑚≤2.6

-12 -11 -10 · · · 4 5 6 -6 -5 -4 · · · 5 6 7