Absolute Value Equations & Inequalities

What is the FIRST step to solving the equation:

|x + 1| = 4

• Set up 2 equations

  x + 1 = 4

  x + 1 = -4

• Subtract 1 on both sides

• Set up 2 equations:

  x + 1 = 4

  x - 1 = 4

• Add 1 to both sides

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

What is the first step to solve the following equation?

-2|x + 3| = -10

• Set up 2 equations

  -2(x + 3) = 10

  -2(x + 3) = -10

• Add 2 to both sides

• Subtract 3 from both sides

• Divide by -2 on both sides

• No Solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

When do you set up 2 equations?

|x + 2| + 3 = 4

• That is the first step.

• After you subtract 3 from both sides.

• After you add 2 and 3.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

−2|−2r − 4| = -12

• {3,1}

• {-5,1}

• {-5,5}

• No Solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3
• c < -5 1/3  or c > 2 2/3
• c < 5 1/3 or c > -2 2/3
• -5 1/3 < c < 2 2/3

Tags

CCSS.HSA.REI.B.3