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SOLVING LINEAR
EQUATIONS
A RC I N STR UC TI ONAL V I DEO
MAT 1 2 0
COL L EG E A LG EBR A
Solving linear Equations
A linear equation in one variable is an equation which can be written
in the form:
ax + b = c
for a, b, and c real numbers with a  0.
Linear equations with one variable:
2x + 3 = 11
2(x  1) = 8  can be rewritten 2x + (2) = 8
Example
Solve:
4(x + 2) + 2 = 3x – 3(2x – 1)
 remove ( ) by applying distributive property
4x + 8 + 2 = 3x – 6x + 3
 combine like terms on each side
4x + 10 = -3x + 3
 transpose like terms to the same side (move terms so that all
variable terms are on one side, and all number terms are on the other
side
Example (continue)
REMEMBER!!
 When you move a term to the other side, you change the sign!
4x + 3x = 3 – 10
7x = -7
x = -7/7
x=-1
Example 2
2
x+5=x-7
3
2x+15=3x-21
-x=-6
x=6
-to clear the fraction you need to multiply each
term by the LCD
Solving absolute value
equations
Whenever you have:
I I = positive number; in this case you will always have two solutions
Example: I x-9 I = 15
Answer: X=-6, x=24
I I = 0; there will be one solution
Example: I y-8 I = 0
Answer: y=8
I I= negative number; there is no solution
Example: I z+7 I = -5
Answer: no solution