Transcript 2.2 Solving Equations

Warm Up
Find the number to make the equation true
1) ___+ 9 = 14
2) ___+27= 35
3) ___-19 = 12
4) 11-___= 19
Simplify each expression
5) -2(3x-8)
6) 8x – 4 – 8x – 9
Review of Distributive Property &
Combing Like Terms
Simplify each expression
3(4 x  6)  7 x
12  3(8  x)
Try It Out
Simplify each expression
7(7  5m)  8(6m  1)
 5(4 x  7)  10 x
2.2 Solving Equations
Standard 5.0: Students solve multistep
problems, including word problems,
involving linear equations and linear
inequalities in one variable and provide
justification for each step.
Solving One-Step Equations
*You must get the variable by itself. You can
move numbers over by using the opposite
operation.
Examples:
x+5=7
x–4=-3
x – (-3) = 10
Try It Out!
Solve the following equations.
1) x + 2 = 7
2) x - 6 = -3
3) x + (-3) = 2
4) x - 5 = -6
2.3 Solving One Step Linear
Equations Using
Multiplication or Division
Standard 5.0: Students solve
multistep problems, including
word problems, involving linear
equations and linear inequalities
in one variable and provide
justification for each step.
1) Solve. -5t = 60
To get the variable by itself, which
number needs to be moved?
-5
To move the -5, you have to do the
opposite operation. What
operation will we use?
division
1) Solve -5t = 60
1.
2.
3.
4.
Draw the line to separate
the equation into 2 sides
Divide both sides by -5
Simplify
Check your answer
-5 -5
t = -12
-5(-12) = 60
1.
2.
3.
4.
2) Solve 24 = 6n
6 6
Draw the line
Divide both sides by 6
4=n
Simplify
Check your answer
24 = 6(4)
3) Solve -3v = -129
1.
2.
3.
4.
v = -126
v = -43
v = 43
v = 126
Answer Now
4) Solve
x
 12
4
You don’t like fractions? Let’s get rid of
them! 
“You can get rid of fractions”
by multiplying both sides of the equation
by the denominator.
1.
2.
3.
4.
x
 12
4) Solve
4
Draw the line
x
Clear the fraction – multiply
4 ·  12 · 4
both sides by 4
Simplify
4
Check your answer
x = -48
48
 12
4
2x
5) Solve
= 18
3
1.
2.
Draw the line
Get rid of the fraction –
multiply both sides by the
reciprocal
2x  5  9
 4x  4  20
Try It Out
3x  5  11
10x  4  34
 4x  8  20
2  (5 x)  13
Examples
x
5  3
3
x7
 10
3
Homework
P. 81 #1-6, 10-11, 13-22
P. 88 #14-19, 28-33, 34-37
P.95 #1-5, 11-22