9.5 Solve Equations by Applying the
Distributive Property
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
Simplify the expressions by applying the Distributive
Property.
1) 7(2x + 5)
2) 9(x − 3) + 2y
3) −2(4x + 7)
4)
−3(x − 8)
Solve Equations by Applying the
Distributive Property
As equations get more complicated can
we us the Distributive Property to
make them simpler?
3(5x + 2) = 36
NOTES
The Distributive Property can be used to remove
parentheses from an equation.
Concept Check
Simplify the equation by applying the distributive
property.
7(x − 2) = 21
2 = 2(4x + 9)
NOTES
Remember that subtraction is the same as "adding the
opposite."
Examples
Solve the equations.
90 = −6(2x + 5)
−(2x + 14) = 8
21 = −3(x − 5)
EXAMPLES
If the area of the rectangle is 90, solve for x.
6
2x + 3
EXAMPLES
Solve the equations.
25 = −2(x + 5) + 7x
EXAMPLES
Solve the equation.
3(2x + 9) + 2(x − 3) = 29
Which equation is
equivalent?
1
(10x − 15) = −12
5
a)2x − 3 = −12
12
b)2x − 3 = −
5
PRACTICE
Solve the equations.
3(5x − 6) − 12x = 6
−2(x − 4) + 3(2x + 8) = 72
1
(12x − 3) = 19
3
PRACTICE
Solve for x if the area of the rectangle is 51.
3
2x - 1
FINAL QUESTION
Solve the equation.
−(x − 2) + 3(2x + 6) = 50