8.9 Clear Fractions from Two-Step
Equations
Common Core Standards
8. EE.7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these
possibilities is the case by successively transforming the given
equation into simpler forms, until an equivalent equation of the form x =
a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including
equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
WARM-UP
Solve the equations.
1
1)
x + 7 = 12
3
2) x + 21 = 36
Evaluate the expressions.
1
3) 3 i
3
4) 3 i 7
5) 3 i 12
Clear Fractions from Two-Step
Equations
How can we get rid of fractions from equations?
1
3 5
x− =
5
5 5
1
3
5
5i x −5i = 5i
5
5
5
x−3 =5
NOTES
To clear fractions from an equation: multiply both sides
by a number that will cancel the denominators and
remove the fractions.
Examples
Clear the fractions and solve the equations.
1
3
x+ =6
4
4
x
5
−3=
7
7
NOTES
For more complex equations, multiply both sides by the
least common multiple of the denominators.
Examples
Solve the equations (hint: answers can be fractions).
1
5 2
x− =
3
6 3
1
5 2
x− =
2
7 7
EXAMPLES
Clear the fractions and solve the equations (hint:
answers can be fractions).
x 1
−
=3
2 10
1
1 5
x− =
3
2 6
EXAMPLES
Which equation is equivalent?
1
1
x+ =4
3
6
2
3
7
x−
=
5
10 10
a)2x + 1 = 4
a) 4x − 3 = 7
b)2x + 1 = 24
b)2x − 3 = 7
c)2x + 6 = 24
c) 4x − 6 = 14
PRACTICE
Write an equivalent
equation with whole
numbers.
1
3
x− =5
8
8
Clear the fractions and
solve the equation.
1
3
x− =5
4
2
PRACTICE
Clear the fractions and solve the equations (hint:
answers can be fractions).
1
5
1
x−
=
7
14 2
1
1 3
x+
=
3
12 4
FINAL QUESTION
Clear the fractions and solve the equations (hint:
answers can be fractions).
1
1 11
x− =
6
8 12