Transcript Solving Multi-Step Equations by Clearing the

Solving Multi-Step
Equations by Clearing
the Fractions
Solving Two-Step Equations That Contain Fractions – Ex. 1
Solve
1
3
x2
2
4
Method: Multiply every term on both sides by the LCD to clear the
fractions.
1
3
Multiply every term on both sides by 4, the
4( x  2  )
2
4
LCD of the fractions.
1
3
4( x)  4(2)  4( )
2
4
2x + 8 = 3
- 8 -8
2x = -5
Distribute 4 on the left and right side.
Simplify.
Since 8 is added to 2x, subtract 8 on
both sides to undo the addition.
Solving Two-Step Equations That Contain Fractions – Ex. 1 (cont.)
Solve
1
3
x2
2
4
Method: Multiply every term on both sides by the LCD to clear the
fractions.
2x = -5
2
2
5
x
2
Since x is multiplied by 2, divide both sides
by 2 to undo the multiplication.
Solving Two-Step Equations That Contain Fractions – Ex. 2
2
1 3
x


Solve 7
7 14
Method: Multiply by the LCD to clear the fractions.
2
1
3
14( x)  14( )  14( )
7
7
14
4x  2  3
+2 +2
4x = 5
4
4
x = 5/4
Multiply every term on both sides by 14,
the LCD of the fractions.
Solving Two-Step Equations That Contain Fractions – Ex. 3
Solve
Method: Multiply by the LCD to clear the fractions.
Multiply both sides by 12, the LCD
of the fractions.
Distribute 12 to every term on both sides.
8r + 9 = 7
–9 –9
8r = –2
Simplify. Since 9 is added to 8r,
subtract 9 from both sides to
undo the addition.
Solving Two-Step Equations That Contain Fractions – Ex. 3 (cont.)
Solve
8r = –2
8
8
Since r is multiplied by 8, divide
both sides by 8 to undo the
multiplication.
Solving Two-Step Equations That Contain Fractions – Ex. 4
Solve
Method: Multiply by the LCD to clear the fractions.
Multiply both sides by 24, the
LCD of the fractions.
Distribute 24 on both sides.
3y – 18 = 14
+18 +18
3y = 32
Simplify.
Since 18 is subtracted from 3y, add
18 to both sides to undo the
subtraction.
Solving Two-Step Equations That Contain Fractions – Ex. 4 (cont.)
Solve
3y = 32
3
3
Since y is multiplied by 3, divide
both sides by 3 to undo the
multiplication.
Solving Two-Step Equations That Contain Decimals – Ex. 5
Solve
0.6x + 2.1 = 4.5
Method: Multiply both sides by the same power of 10 to
clear the decimals.
Multiply every terms on both sides by 10
10(0.6x) + 10(2.1) = 10(4.5) because all decimals are to the tenths place.
6x+ 21 = 45
–21 -21
6x = 24
6
6
x=4
(If decimals were to hundredths place, you would
multiply by 100.)
Review
Find the least common multiple (LCM) of the
following numbers:
3, 5
4, 8
2, 3, 6
Solving Two-Step Equations That Contain Fractions – Ex. 1
Solve
1
3
x2
2
4
Method: Multiply every
term on both sides by the
LCD to clear the fractions.
Solving Two-Step Equations That Contain Fractions – Ex. 2
2
1 3
x


Solve 7
7 14
Method: Multiply by the LCD to clear the fractions.
Solving Two-Step Equations That Contain Fractions – Ex. 3
Solve
Method: Multiply by the
LCD to clear the fractions.
Solving Two-Step Equations That Contain Fractions – Ex. 4
Solve
Method: Multiply by the
LCD to clear the fractions.
Solving Two-Step Equations That Contain Decimals – Ex. 5
Solve
0.6x + 2.1 = 4.5
Method: Multiply both
sides by the same power of
10 to clear the decimals.