Transcript 10 Questions & Answers[1].

10 Questions & Answers
Absolute value equations and inequalities
Solving linear equations and inequalities
* If you want to know how to solve these ten
questions do it on a separate sheet of paper.
Try solving them to the best of your abilities
before clicking to see the answers.
Solving absolute value equations and
Inequalities
• Goal 1: solving equations and
inequalities
• Absolute value of a number x, is written like
this IxI, is the distance the number is from 0
on a number line. Always remember absolute
value is always nonnegative.
The distance
between -4
and 0 is 4, so
I-4I=4
The distance
between 4 and
0 is 4, so I4I=4
•
Lets start with some
examples…
Rewrite the absolute
value equation as two linear equations
and then solve each linear equation.
• Ex 1) Solve I2x-5I=9
• I2x-5I=9
Write original equation
• 2x-5=0
-9
or
2x-5=-9
• 2x=14
or
2x=-4
• X=7
or
x=-2
expression can be 9 or
add 5 to each side
divide each side by 2
Lets try 2 one your own…
•Rewrite the absolute value equation as two linear equations.
• Ex 2) solve I5n4I=16
• Check your answer
after you finished
solving.
• 5n-4=16 or 5n4=-16
• 5n=20
12
or
• n= 4
12/5
or
Ex 3) solve I 8x+1I=23
Check your answer after
you finished solving.
• 8x=1=23
or 8x=1=-23
• 8x=22
or
8x=-24
• X= 22/8
or
x= -3
5n=-
n= -
Practice makes perfect…
• Rewrite the absolute value equation as two linear equations.
1. Ix+5I=4
2. Ix-3I=2
3. I3x+4I=2
0
4. I4x• Decide
whether the given number is a solution of the
7I=13
equation.
5. I3x+8I =20: -4
6. I2x-9I= 11: -1
7. I-x+9I = 4: -5
8. I3x+6I = 0: -2
Answers
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1. x= -1,-9
2. x= 5,1
3. x=16/3,-8
4. x= 5, -3/2
5.no
6. yes
7.no
8. yes