Algebra 1 homework help

Absolute Values

Problem:
Solve the equation |x - 4| = 10

Solution:
There are two possibilities

Either x - 4 = 10 ⇒ x - 4 + 4 = 10 + 4 ⇒ x = 14						Or -(x - 4) = 10 ⇒ -x + 4 = 10 ⇒ -x + 4 - 4 = 10 - 4 ⇒ -x = 6 ⇒ x = -6
Therefore x = 14, -6
Alternatively, you could use the number line method to solve this problem. Here's the video lesson.

Problem:
Solve the equation |y + 5| = 12

Solution:
There are two possibilities

Either y + 5 = 12 ⇒ y + 5 - 5 = 12 - 5 ⇒ y = 7						Or -(y + 5) = 12 ⇒ -y - 5 = 12 ⇒ -y - 5 + 5 = 12 + 5 ⇒ -y = 17 ⇒ y = -17
Therefore y = 7, -17
Once again, you could have used the number line to solve this problem: \|y + 5\| = 12 ⇒ \|y - (-5)\| = 12 which means y is 12 units away from -5 on the number line, on either side of it

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Problem:
Solve the equation |7 - z| = 9

Solution:
There are two possibilities

Either 7 - z = 9 ⇒ 7 - z - 7 = 9 - 7 ⇒ - z = 2 ⇒ z = - 2						Or -(7 - z) = 9 ⇒ - 7 + z = 9 ⇒ - 7 + z + 7 = 9 + 7 ⇒ z = 16
Therefore z = -2, 16
Using the number line: \|7 - z\| = 9 means 7 is 9 units away from z on the number line, on either side of it

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Problem:
Solve the equation 2|p + 6| - 8 = 20

Solution:
Solve for |p + 6| first and then consider the possibilities
2|p + 6| - 8 = 20
⇒ 2|p + 6| - 8 + 8 = 20 + 8
⇒ 2|p + 6| = 28
Divide both sides by 2
|p + 6| = 14

There are two possibilities now

Either p + 6 = 14 ⇒ p + 6 - 6 = 14 - 6 ⇒ p = 8								Or -(p + 6) = 14 ⇒ -p - 6 = 14 ⇒ -p - 6 + 6 = 14 + 6 ⇒ -p = 20 ⇒ p = -20
Therefore y = 8, -20
Number line solution: \|p + 6\| = 14 ⇒ \|p -(-6)\| = 14 which means p is 14 units away from -6 on the number line, on either side of it

For two or more equations involving absolute value, this example should help.

Algebra 1 homework help list