3.7 Absolute value

DAY 2

Solve for x----no notes on this slide (just watch).

|x| = 5

|x + 2| = 5

x = 5 or x = -5

x + 2 = 5 or x + 2 = -5

x = 3 - 2 -2 - 2 -2

x = -7 check

|3 + 2| = 5 |-7 + 2| = 5check

Solve for x---again no notes on this slide.

|x + 4| = 7x + 4 = 7 or x + 4 = -7

x = 3 -4 -4

Check with the original equation.

|(x) + 4 | = 7

Check with the original equation.

- 4 -4 x = -11

| (x) + 4 | = 7|(-11) + 4 | = 7

|-7 | = 7|(3) + 4 | = 7|7 | = 7

Your answers are:

3, -11

Solve for x

|2x + 5| = 132x + 5 = 13 or 2x + 5 = -13

2x = 8 - 5 -5

Check with the original equation

|2(4) + 5 | = 13Check with the original equation

x= 4

- 5 -5 2x = -18

x= -9

|2(-9) + 5 | = 13|-18 + 5 | = 13

|-13 | = 13|8 + 5 | = 13|13 | = 13

Your answers are:

4, -9

|-2x + 5| - 4 = 9

-2x + 5 = 13 or -2x + 5 = -13

-2x = 8 -5 -5

Check with the original equation.

|-2(-4) + 5 | - 4 = 9

Check with the original equation.

- 5 - 5 -2x = -18

|-2(9) +5 | - 4 =9|(-18) + 5 | -4 = 9

|-13 | -4 = 9|(8) + 5 | - 4 = 9|13 | - 4 = 9

Solve for x

|-2x + 5| =13

The answers are -4, 9 x = -4 x = 9

13 -4 = 9

+9+9|-2x - 6| - 9 = 11

-2x – 6 = 20 or -2x - 6 = -20

-2x = 26 +6 +6

Check with the original equation.

|-2(-13) - 6 | - 9 = 11

Check with the original equation.

+6 +6 -2x = -14

|-2(7) - 6| -9 = 11|(-14) -6 | -9 = 11

|-20 | - 9 = 11|(26) - 6 | - 9 = 11

|20 | - 9 = 11

Solve for x

|-2x - 6| =20

The answers are -13, 7 x = -13 x = 7

20 - 9 = 11

Solve for x 2|x + 4| = 14

x + 4 = 7 or x + 4 = -7

x = 3 -4 -4

Check with the original equation.

2|(x) + 4 | = 14

Check with the original equation.

- 4 -4 x = -11

2| (x) + 4 | = 142|(-11) + 4 | = 14

2|-7 | = 142|(3) + 4 | = 142|7 | = 14

Your answers are:

3, -11

2 2

|x + 4| = 7

|x| + 2 = 7

Solve for x and then graph the solutions.

- 2 -2

|x| = 5

x =5 or x = -5

-5 0 5

|x| > 2

Solve for x and then graph the solutions.

-5 0 5

Assignment: page 211:17-20, 26-28,31, 49,53-55

| A| < b | A| > b

-5 0 5

-b < A < b

Solving absolute value inequalities

A < -b or A > b

| x – 1 | < 2 -2 < x – 1 < 2

-2 < x – 1 and x -1 < 2+1 + 1

-1 < x

+1 + 1

x < 3

| x – 1 | > 2

x – 1 < -2 OR x -1 > 2+1 + 1

x < -1

+1 + 1

x > 3

-5 0 5

Solve and graph the following: |2x + 1| > 9

| A| < b | A| > b

-b < A < b A < -b or A > b|2x + 1| > 9

2x + 1 < -9 OR 2x +1 > 9 -1 -1

2x < -10 x < -5

-1 -12x > 8 x > 4

-10 -5 0 5 10

Assignment: page 211: 24-30 evens; 32-40 all; 50-60 evens

If it says graph, graph it