Download 8.8 Solve Two-Step Equations With Fractions or Decimal Solutions

8.8 Solve Two-Step Equations With
Fractions or Decimal Solutions
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 equation.
1) 2x + 6 = 7
Evaluate the expressions.
2) 9 ÷ 2
3) 10 ÷ 3
Solve Two-Step Equations With Fractions
or Decimal Solutions
Can two-step equations have fraction or decimal
solutions?
4x + 9 = 16
− 9 = −9
4x
= 7
4
4
x
7
= or 1.75
4
NOTES
When answers are not integers they can be expressed
as either fractions or decimals.
Examples
Find the solutions. Express answers as both
fractions and decimals.
2x − 7 = 12
18 = −5x − 3
NOTES
We always have to simplify, but don't always have to
make improper fractions mixed numbers.
Examples
Find the solutions.
8x + 1 = 3
19 = −4x + 9
NOTES
With repeating decimals it is usually easier to choose
fractions.
Examples
Find the solutions.
3x + 4 = 17
4 = 6x − 9
EXAMPLES
Solve the equation.
6x − 3 = 4
7
a)
6
1
b)
2
7
c)
3
5
d)
5
EXAMPLES
Solve the equation.
14 = −4x − 1
a) − 3
b) − 3.25
c) − 3.5
d) − 3.75
PRACTICE
Find the solutions. Express answers as both fractions
and decimals.
−5x − 7 = −4
14 = 9x + 8
FINAL QUESTION
Find the solution. Express answer as both fractions and
decimals.
12 + 10x = 27