1-6Day 1

Absolute Value Equations

Objective:

I can solve an absolute value equation.

Unit 1

Distance from zero on the number line → distance from x to 0 is a units

x

Absolute Value

− a a0

|2 𝑥−1|=5

2 𝑥−1=−5 2 𝑥−1=5or

2 𝑥=− 4𝑥=−2

2 𝑥=6𝑥=3

Solve and Graph|3 𝑥+2|=4

3 𝑥=2

𝑥=23

3 𝑥+2=43 𝑥+2=4

𝑥=−2

3 𝑥=− 6

23

−2 0

or

Solve for x and graph3|𝑥+2|−1=8 2|𝑥+9|+3=7

3|𝑥+2|=9

|𝑥+2|=3

𝑥+2=− 3𝑥+2=3 𝑥=1

2|𝑥+9|=4

|𝑥+9|=2

𝑥+9=−2𝑥+9=2 𝑥=−7

1−5 0 −7−11 0

𝑥=−5

.. ..𝑥=−11

Warning: Check your solutions|3 𝑥+2|=4 𝑥+5

3 𝑥+2=−(4 𝑥+5) 3 𝑥+2=4 𝑥+5or

3 𝑥+2=− 4 𝑥−5

𝑥=−1

−3=𝑥7 𝑥=−7

|3 (−1)+2|=4 (−1)+5

|− 1|=1

|3 (−3)+2|=4 (− 3)+5

|− 7|=−7

Extraneous solution

p.46:10-24

1-6Day 2

Absolute Value Inequalities

Objective:

I can solve an absolute value inequality.

Absolute Value Inequality

|2 𝑥−1|<5

2 𝑥−1<5−5<¿

− 4<2𝑥<6

−2<𝑥<3

+1 +1+1

2 2 2

-3 -2 -1 0 1 2 3 4 xxx

−𝑎<𝑥<𝑎0 x𝑎−𝑎

|3 𝑥− 4|≤ 8

x

−43

≤𝑥≤ 4

Absolute Value Inequality

|2 𝑥+4|≥ 6

2 𝑥+4≥ 62 𝑥+4≤ − 6

𝑥≥ 1 𝑥≤ −5

or |5 𝑥+10|>15

or

or

-6 -5 -4 -3 -2 -1 0 1 2 xxx

𝑎−𝑎 0 x

or

-6 -5 -4 -3 -2 -1 0 1 2 x

and

Compound InequalitiesAnd inequalities

Or inequalities3<5𝑥−2<73<5𝑥−2 5 𝑥−2<7+2 +2 +2+2

5<5 𝑥 5 𝑥<95 5 5 51<𝑥 𝑥<

95

0 2 xxx

7 𝑥− 3>18 3 𝑥− 2≤ − 2+3 +3 +2 +27 𝑥>21 3 𝑥≤ 07 7 33𝑥>3 𝑥≤ 0

or

0 2 4 xxx

p.38:37-43 odd

or and

p.46: 25-35

odd, 57-65

odd