Transcript PPT - Militant Grammarian

Absolute Value Equations
SEI.3.AC.1SLE 1: Solve, with and without appropriate
technology, multi-step equations and inequalities with
rational coefficients numerically, algebraically and
graphically
Students will be able to solve absolute value equations
and inequalities, and be able to graph them.
Absolute Value
• All integers are composed of two parts – the size
and the direction. For example, +5 is five units in
the positive direction; –5 is five units in the negative
direction.
• The absolute value {written like this: 5 }of a
number gives the size of the number without the
direction. For example, 5 = 5 and 5 = 5. The
answer is always positive.
• Conversely, if you have an equation x  5 , the
answer could be 5 or –5. You will have 2 answers.
FHS
Equations and Inequalities
2
Absolute Value Equations
To solve absolute value equations, we follow the same
procedures that we do in solving any equation.
Solve for the absolute value first. Set up the two
solutions, and solve them for the variable.
x3 2  6
Here are some examples:
2  2
x3 8
x 3 7
3  3
x 4
x  3  8 or x  3  8
x  4 or x  4
FHS
x  11 or x  5
Equations and Inequalities
3