Download 8.1 Solve Equations that Contain Addition and Subtraction

8.1 Solve Equations that Contain
Addition and Subtraction
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
Fill in the blank.
1) _____ + 3 = 7
2) 19 = ____ + 10
3) _____ − 8 = 1
4) 10 = ____ − 6
Find x.
5)
x + 7 = 12
6)
x − 1 = 14
Solve Equations that Contain
Addition and Subtraction
How do we figure out the missing
number when we can't do the problem
in our head?
476 = x + 318
1.6 = x − 2.37
NOTES
Addition and subtraction are called inverse operations
because they undo each other.
Concept Check
Evaluate the expressions.
13 + 5 − 5
Simplify the expression.
x+4−4
17 − 2 + 2
NOTES
The Properties of Equality – Any operation done to one
side of an equation must be repeated exactly on the
other side for the equation to remain true.
Concept Check
Are the equations true?
4 + 7 = 11
4 + 7 − 7 = 11 − 7
4 + 7 = 11 − 7
NOTES
To solve one-step equations perform the inverse
operation to both sides to get x by itself.
Examples
Solve the equation.
x + 15 = 37
x − 9 = 43
17 = x + 8
38 = x − 18
NOTES
The answer to an equation is called the solution.
Examples
Find the solution.
x + 3.2 = 7.9
18.7 = x + 5
x − .8 = 4.7
EXAMPLES
If the perimeter is 24.5 inches, write and solve an
equation to find its missing length.
8 in
8in
x
PRACTICE
Solve the equations.
x − 68 = 159
43.7 = x + 6.5
24.4 = x − 3
17 = x + 1.3
PRACTICE
Find the missing length if the perimeter is 30
centimeters.
5 cm
x
12 cm
FINAL QUESTION
Find the solution.
x − 136 = 18.1