Solve & Graph Absolute Value Inequality

Remember … Solve: |4x – 1| - 4 = 3 |4x – 1| = 7 4x – 1 = -7 4x – 1 = 7 4x = -6 x = 4x = 8 x = x = 2 Check: ✔✔

Today’s Inequality: |4x -1| - 4 < 3 Is yesterday’s equality:|4x – 1| - 4 = 3 Take the graph from the prior screen: and test each section: test -5 |4(-5) – 1| - 4 < 3 |-20 – 1| - 4 < 3 |-21| - 4 < 3 21 – 4 < 3 17 < 3 ✗ test 0 |4(0) – 1| - 4 < 3 |0 – 1| - 4 < 3 |-1| - 4 < 3 1 – 4 < 3 -3 < 3 ✔ test 5 |4(5) – 1| - 4 < 3 |20 – 1| - 4 < 3 |19| - 4 < 3 19 – 4 < 3 15 < 3 ✗

|12 - 4x| + 2 > 6 Solve: 12 – 4x = -4 -4x = -16 x = 4 Check: |12 – 4(4)| + 2 = 6 test 0 |12 – 4(0)| + 2 > 6 |12 – 0| + 2 > 6 |12| + 2 > > 6 14 > 6 test 3 ✗ test 5 ✔ |12 – 4x|+2 = 6 |12 – 4x| = 4 12 – 4x = 4 -4x = -8 x = 2 |12 – 16| + 2 = 6 |-4| + 2 = = 6 6 = 6 |12 – 4(2)| + 2 = 6 ✔ |12 – 8| + 2 = 6 |4| + 2 = = 6 6 = 6 ✔ |12 – 4(3)| + 2 > 6 |12 – 12| + 2 > 6 |0| + 2 > > 6 2 > 6 |12 – 4(5)| + 2 > 6 |12 – 20| + 2 > 6 |-8| + 2 > > 6 10 > 6 ✔

Try: 3|2x – 2| + 2 > 8 Solve: 3|2x – 2| = 6 |2x – 2| = 2 2x – 2 = 2 2x – 2 = -2 2x = 0 x = 0 2x = 4 x = 2 Check: ✔ ✔ 3|2(0) – 2| = 6 3|0 – 2| = 6 3 |-2| = 6 3(2) = 6 6 = 6 3|2(2) – 2| = 6 3|4 – 2| = 6 3 |2| = 6 3(2) = 6 6 = 6 test -5 3|2(-5) – 2| +2 > 8 3|-10 – 2| + 2 > 8 3|-12| + 2 > 8 3(12) + 2 > > 8 38 > 8 ✔ test 1 3|2(1) – 2| +2 > 8 3|2 – 2| + 2 > 8 3|0| + 2 > 8 3(0) + 2 > > 8 2 > 8 ✗ test 5 3|2(5) – 2| +2 > 8 3|10 – 2| + 2 > 8 3|8| + 2 > 8 3(8) + 2 > > 8 26 > 8 ✔ 3|2x – 2| + 2 = 8

It is written … When working with absolute value inequalities, If the sign is < or < (less thAND) The graph will look like If the sign is > or >(greatOR than) The graph will look like and is written# < x < # and is writtenx #

What does absolute value mean?