2.2
More Solving Equations
Homework: Odds 1
– 69
| Nancy J. McCormick's Home Page | DSPM 0800 Class Notes |
Process:
Remove parentheses.
Combine like terms on each side of the
equation.
Clear fractions and/ or decimals (optional).
Add to or subtract from each side of the
equation to get the variable term alone on one side of the equation only.
Divide or multiply each side of the equation
to get the coefficient of the variable equal to one.
Example: 4x + 3 = -21
4x = -24 Subtracted 3
from each side.
x = -6 Divided
each side by 4.
Check:
4(-6) + 3 = -21
-24 +
3 = -21
-21 = -21
Example:5y
– 7 + y = 7y + 21 – 5y
6y – 7 = 2y + 21 Combined like terms on
each side.
4y – 7 =
21
Subtracted 2y from each side.
4y =
28
Added 7 to each side.
y =
7
Divided each side by 4.
check:
5( 7
) – 7 + ( 7 ) = 7( 7 ) + 21 – 5( 7 )
35
– 7 + 7 = 49 + 21 – 35
35 = 70 – 35
35 = 35
Example:
6x – (3x + 8) = 16
6x – 3x – 8 = 16
Removed parentheses by distributing –1.
3x – 8 = 16 Combined like
terms.
3x = 24 Added 8 to each side.
x
= 8 Divided each side by 3.
Example:
5 – 3(x + 2) = 5
5 – 3x – 6 = 5 Removed parentheses by
distributing –3.
-1 – 3x =
5
Combined like terms.
- 3x =
6
Added 1 to each side.
x
=
-2
Divided each side by –3.
Example:
Multiplied each term by 15 to clear fractions.
Combined like terms.
Added 10y to each side.
Subtracted 36 from each side.
Divided each side by 7.
Example:
1.7a + 8 – 1.62a = 0.4a – 0.32 + 8 (2 or less decimal
places in each term.)
170a + 800 – 162a = 40a – 32 + 800 Moved decimal 2
places in each term.
8a + 800 = 40a + 768 Combined like
terms.
800 = 32a +
768 Subtracted 8a from each side.
32 =
32a
Subtracted 768 from each side.
1 =
a
Divided each side by 32.
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