Absolute Value Equations and Extraneous Solutions

Solve: | x + 3 | ≤ 2

Hint: Remember to split it in to two inequalities and flip the symbol and sign on the second inequality.

• No Solution
• All Real Numbers
• -5 ≤ x ≤ -1
• 1 ≤ x ≤ 5

| 2x + 12 | < 8

Which is the correct first step?

• 2x + 12 < 8 and 2x+12 > -8

• 2x + 12 < 8 or 2x+12 > -8

• 2x + 12 < 8 and 2x+12 < -8

• 2x + 12 < 8 or 2x+12 < -8

What is the correct first step?

• divide by 10
• multiply by 10
• make it two inequalities with an "or"
• make it two inequalities with and "and

What is the solution of ∣5x-2∣=7x+14?

Hint: Make sure you make BOTH parts of 7x + 14 negative when you separate in to two equations. ALSO check for extraneous solutions

• x=-1

• x=-1, x=-8

• x=-8

• no solutions

There are two ways to get a ticket while driving on the highway. You can get a ticket if you are driving slower than 45 mph. You can also get a ticket if you're driving faster than 75 mph. Which compound inequality matches this scenario?

• x > 45 and x <75

• x > 45 or x < 75

• x < 45 and x > 75

• x < 45 or x > 75

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Which compound inequality represents this graph:

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Solve: 4x < 2x + 6 or -5x - 4 < -29

• x < 3 or x < 5

• 3 < x < 5

• x < 3 or x > 5

• 5 < x < 3

Which graph represents the solution to 5x < 10 or x + 3x > 20?

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• No solution

• One solution

• Two solutions