Solving Inequalities Is It a Solution

On the interstate for someone to get a ticket for speed, they must be less than 45 mph or greater than 75 mph. What absolute value inequality describes the speeds of those receiving a ticket?

• |x - 120| less than or = 30

• |x - 60| less than or = 15

• |x + 120| greater than or = 30

• |x - 60| greater than or = 15

Which compound inequality represents the graph?

• m < -1 OR m > 2

• -1 < m < 2

• m > -1 OR m < 2

• 2 > m > -1

What is the correct first step?

• divide both sides by 10

• multiply both sides by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and" or a between statement

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and" or a between statement

• separate into two inequalities with an "or" statement

• divide both sides by -8

• add 8 to both sides

What is ALWAYS the first GOAL in solving an absolute value inequality?

• set up the positive case

• set up the negative case

• isolate the absolute value expression

• multiply or divide by the coefficient of the variable

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5 ... 1 ≤ x ≤ 5

| x + 3 | > 8

• No Solution

• All Real Numbers

• x < -11  or  x > 5

• -5 < x < 11

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

Solve for n.

• n ≥ 10 and n ≤ -6

• n > 10 and n < -6

• n ≥ 10 or n ≤ -6

• n > 10 or n < -6