Linear and Absolute Value Equations

Solve the following equation:

|−4 + 5x| = 16

• {16/5,12/5}

• {4, −5}

• {−12/5, 4}

• {4}

Solve the following equation:

|2a + 10| = 6

• a = 8, a = 2

• a = −2

• a = −8

• a = −8, a = −2

Solve the following equation:

|v + 8| − 5 = 2

• {−1, −15}

• {−1, −5}

• {−15, 15}

• No Solution

Solve the following equation:

−2|−2r − 4| = −12

• {3, 1}

• {−5, 1}

• {−5, 5}

• No Solution

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

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

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.

• x = -2

• x = 1

• x = 4

• x = -8

A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.

• c = 2.75b + 4
• c = 2.75b
• c =  4b- 2.75
• c = 2.75b - 4