Download 13.5 Solve Two-Step Equations and Inequalities with Fractions

13.5 Solve Two-Step Equations and
Inequalities with Fractions
Common Core Standards
7.EE.4. Use variables to represent quantities in a real-world or mathematical
problem, and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms
fluently. Compare an algebraic solution to an arithmetic solution, identifying the
sequence of the operations used in each approach. For example, the perimeter of a
rectangle is 54 cm. Its length is 6 cm. What is its width?
b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the
inequality and interpret it in the context of the problem. For example: As a
salesperson, you are paid $50 per week plus $3 per sale. This week you want your
pay to be at least $100. Write an inequality for the number of sales you need to make,
and describe the solution.
WARM-UP
Solve the two-step equations and inequalities.
1) 3x − 7 > −40
2) −17 =
Find the reciprocal.
3) 5
4) 1
3
6
x
− 10
6
Solve Two-Step Equations and
Inequalities with Fraction
Coefficients
Can we use the Inverse Property of
Multiplication to help us solve
equations?
1 7
g =1
7 1
NOTES
To remove a fraction coefficient multiply both sides by
the reciprocal during step 2. Step 1 remains the same.
Examples
Solve the equations and inequalities.
1
x + 6 < 16
2
1
x−3= 4
5
EXAMPLES
Solve the equations and inequalities.
2
x−8≥2
5
9
x + 12 = 21
2
NOTES
The formula to convert Fahrenheit temperatures into
Celsius is…
9
C + 32 = F
5
Example
The temperature is 50o Fahrenheit. What is the
temperature in Celsius?
EXAMPLES
Use the formula to convert 68o Fahrenheit into Celsius.
9
C + 32 = F
5
NOTES
It doesn’t matter where the negative sign is in the
fraction.
Examples
Solve the equations.
1
− x+5=7
4
−2
2=
x−6
7
PRACTICE
Solve the equations and inequalities.
1
x−6>5
3
2
−8 = x − 2
5
Use the formula to convert 104o Fahrenheit into Celsius.
9
C + 32 = F
5
PRACTICE
A sunflower grows a rate of ¼ foot per week. When it
was planted in the ground it was 2 feet tall. If the
sunflower is currently 5 feet tall, write and solve a twostep equation to determine the age in weeks (w) of the
flower.
FINAL QUESTION
Solve the inequality (hint: do we need to flip the symbol?)
5
− x+7<2
8