Download Linear Equations

LINEAR EQUATIONS
SOLVING LINEAR EQUATIONS



Solving equations is the same
is finding out what “x” is.
You do that by working the
problem backwards.
NO GUESS AND CHECK!!!

7x + 8 = 22
-8 -8
7x = 14
7𝑥
14
=
7
7
x=2
1. Subtract 8 from both
sides.
2. Divide both sides by 7.
3. Check your answer by
plugging it back in for
“x”.
SOLVING LINEAR EQUATIONS
-6x – 15 = -3
+15 +15
- 6x = 12
−6𝑥
12
=
−6
−6
x=-2
9x – 8 = 22
+8 +8
9x = 30
9𝑥
30
=
9
9
x=
30
9
x=
10
3
Yes, the answers can be negative or fractions!
LINEAR EQUATIONS

Some equations have
variables on both sides!
3x + 14 = 5x – 8
-3x +8
-3x +8
22 = 2x
x = 11
7x – 12 = 5x + 9
-5x +12 -5x + 12
2x = 21
x=
21
2
You need to get all the variables
to one side and all the plain
numbers to the other.
Then solve like any other
equation.
How do you know which way to
go???
Don’t forget to check your
answers!
LINEAR EQUATIONS

Some involve multiple steps.
Just take it one step at a
time!
5(x + 4) – 6 = 3 – 2(3x – 4)
5x + 20 – 6 = 3 – 6x + 8
5x + 14 = -6x + 11
11x = - 3
x=
−3
11
1. Distribute.
2. Combine like terms.
3. Get variables to one
side and numbers to
the other.
4. Finish it up!
LINEAR EQUATIONS

What about this?
1
3
2
𝑥+4= 𝑥 −
3
7
21
1
3
2
 ( 𝑥+4=
𝑥 − )21
3
7
21




7x + 84 = 9x – 2
86 = 2x
x = 43
The easiest way to solve this
is to get rid of all of the
fractions.
How??
Multiply the whole equation
by the largest denominator.
Why??
The fractions will simplify
into to whole numbers and
leave you with a linear
equation.
LINEAR EQUATIONS

Try again!
2
4
2
𝑥 + = 5𝑥 −
3
5
15
2
4
2
 ( 𝑥+
= 5𝑥 − )15
3
5
15


10x + 12 = 75x – 2
 14 = 65x

x=
14
65
LINEAR EQUATIONS
𝑥
5
𝑥

− 3𝑥 = +
7
4
28
𝑥
5
𝑥
 ( − 3𝑥 =
+ )28
7
4
28




4x – 84x = 35 + x
-80x = 35 + x
-81x = 35
x=−
35
81
LINEAR EQUATIONS
Practice!!
 1. 5x + 3 = 8
 2. 7x – 19 = 2
 3. 8x + 8 = 7x – 2
 4. -4x – 5 = 9x + 15
 5. 4(x + 8) – 9 = -2(x – 5) – 15
 6. 7x – 3(2x + 14) = 4(3x – 7) + 8

LINEAR EQUATIONS



1.
2.
3.
2𝑥
5
𝑥
3
−7=
+
7𝑥
8
+
2
9
3
+
10
= 7𝑥 −
5
16
=
−3
2
How did you do??
Show me your answers!
5𝑥
5
18
− 2𝑥 +
3𝑥
4
1. x =
−73
46
2. x =
3
40
3. x =
−29
34
9
120
𝑖𝑓 𝑦𝑜𝑢 𝑓𝑜𝑟𝑔𝑜𝑡 𝑡𝑜 𝑠𝑖𝑚𝑝𝑙𝑖𝑓𝑦