Algebra 1 homework help

Absolute Values

Algebra 1 homework help on other topics

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

Click here for more Math homework help options
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

For more free Algebra 1 homework help click here
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