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324 1.3 solvinglinearequations
1. Notes Over 1.3
It’s time to stop
“daydreaming”
and start applying
“mental math”
2. 231 −−= x.
Notes Over 1.3
Variable on One SideVariable on One Side
Solve the equation.
2+2+
x−
6182 +=− y.
6− 6−
24−
593 =− z.
=5
5−=x y=
9− 9−
z− 4−=
4=z
3. 12664 −=+ x.
Notes Over 1.3
Variable on One SideVariable on One Side
Solve the equation.
6−6−
18−
1525 =−x.
5+5+
x2=x6
3−=x
6=
6 6 2 2
3=x
2
3
6 =−
x
. (3− ) 3−
6−=x
4. 1643157 +−=− aa.
Notes Over 1.3
Variable on Both SideVariable on Both Side
Solve the equation.
a4+a4+
1=a
15− 15−
624638 +=+− mm.
m3+ m3+
m27=0
6−6−
2727
0=m
5. 37649 +=− ss.
Notes Over 1.3
Variable on Both SideVariable on Both Side
Solve the equation.
s4− s4−
s3=−9
3−3−
33
3−=s
6. ttt 2101810 −=+−.
Notes Over 1.3
Variable on Both SideVariable on Both Side
Solve the equation.
t2+t2+
9=t9
1− 1−
9 9
1=t
tt 21017 −=+
7. 72411 +=− xx.
Notes Over 1.3
Variable on Both SideVariable on Both Side
Solve the equation.
x− x−
x=−11
7−7−
xx 1624412 +=.
x16−x16−
24=− x12
12− 12−
2−=x
8. ( ) ( )221235.13 −−=+− xx
Notes Over 1.3
Using the Distributive PropertyUsing the Distributive Property
Solve the equation.
x5
x2+x2+
7=x7
3+ 3+
7 7
1=x
1215+− x2−= 4+
4235 +−=− xx
9. ( ) ( ) 7132414 =++−− kk.
Notes Over 1.3
Using the Distributive PropertyUsing the Distributive Property
Solve the equation.
k4−
4−=− k
11− 11−
4=k
8+ k3+ 73 =+
k− 711=+
10. ( )12215 +=− xx.
Notes Over 1.3
Using the Distributive PropertyUsing the Distributive Property
Solve the equation.
x2−
2=− x4
x2−x2−
x2= 2+
4− 4−
2
1
−=x
11. ( )529316 −=− xx.
Notes Over 1.3
Using the Distributive PropertyUsing the Distributive Property
Solve the equation.
93 −x
1−=x
x2−x2−
x2= 10−
9+ 9+
12. ( )25
3
2
617 −= nn.
Notes Over 1.3
Solving an Equation with FractionsSolving an Equation with Fractions
Solve the equation.
n10−n10−
4−=n8
8 8
2
1
−=n
=n18 n10 4−
13. 41
4
3
18 =+x.
Notes Over 1.3
Solving an Equation with FractionsSolving an Equation with Fractions
Solve the equation.
4− 4−
12=x3
3 3
4=x
x3 =+ 4 16
(4 )4(4
14. xx 4
3
2
2
1
19 =−.
Notes Over 1.3
Solving an Equation with FractionsSolving an Equation with Fractions
Solve the equation.
x3− x3−
x21=− 4
2121
21
4
−=x
3
=− 4 x24
(6 )6(6
x3
2
15. 1
3
2
5
3
20 += xx.
Notes Over 1.3
Solving an Equation with FractionsSolving an Equation with Fractions
Solve the equation.
x10−x10−
15=− x
15−=x
3
x10= 15+
(15 )15(15
x9
5
