Download Absolute Value Equations Absolute Value Equations: , is an

Absolute Value Equations
Absolute Value Equations: x  4 , is an equation that contains an absolute value
expression.
The equation x  4 means that the distance between 0 if 4. The solutions of
the equation
are 4 and -4, because they are the only numbers whose distance
from 0 is 4.
Solving an 
Absolute Value Expression
The equation ax  b  c where c  0 is equivalent to the statement ax+b=c or
ax+b=-c
Solve an absolute value equation:


Solve x  3  8
To solve, rewrite the absolute value equation as 2 equations. Then
solve each equation separately.

x 38
x  3  8
or
x  11
x  5
The solutions are 11 and -5.
Check your answer by plugging
 and chugging both numbers.

Try This: x  4  3
When solving multi-step equations, you cannot solve work on numbers inside the
absolute value symbol until you get all other numbers out of the equations first

Example: Solve 32x  7  5  4
First get the absolute value by itself

32x  7  5  4
32x  7  9
2x  7  3
Then solve the absolute value equation:
2x  7  3 
2x  10
2x  7  3
or
2x  4
x5
x2
The solutions are 5 and 2.


Try This: 4 t  9  5  19
No Solutions: The absolute value of a number is never negative. So, when an
absolute value expression equals a negative number, there are no solutions.

3x  5  6  2
Example:
3x  5  8
Because the solution is -8, there are no solutions.
Absolute
 deviations: For a number from a given value is the absolute value of the
difference of x and the given value.
Absolute Deviation= x  givenvalue
Example: Before the start of a professional basketball game, a basketball must be
inflated to an air pressure of 8 pounds per square inch (psi) with an absolute error
of 0.5 psi. find the 
minimum and maximum acceptable air pressures for the
basketball.
0.5  p  8
0.5=p-8
 8.5=p
or
-0.5=p-8
7.5=p
The minimum and maximum acceptable pressures are 7.5 psi and 8.5 psi.
Try These:
2m5  4 2
3 n  2  7  10

The absolute deviation of x from 7.6 is 5.2. what are the values of x that
satisfy the requirement?