Download MA.7A.A.3.3 Formulate and use different strategies to solve one

MA.7A.A.3.3 Formulate and use different strategies to solve one-step and two-step linear equations, including
equations with rational coefficients.
Instructions and Examples
Vocabulary:
Equation- mathematical sentence showing two expressions are equal.
Solution- value for a variable.
Solving Equations
To solve two-step equations, you can balance the equation by getting the variable by itself. First, undo any
addition or subtraction. Then undo the multiplication or division.
n
–2= 5
4
8y -2 = 18
+2 = +2 Add 2 to both sides.
+2 = +2 Add 2 to both sides to keep the equation balanced
n
8y = 16
=7
8
8 Divide both sides by 8 to get the variable alone on one side.
4
y =2
 4 =  4 Multiply 4 by both sides.
n
= 28
Check your work: If y=2, the 8∙2 – 2 = 18
18 = 18 √
If your variable is being multiplied by a fraction, you can multiply both sides by the reciprocal of that fraction.
2
4
t
3
9
2 3
3
the reciprocal of is
so multiply both sides by
3 2
2
Remember – to multiply fractions, simply
4  3  the numerators and multiply the
3 2
  t  multiply
 
9denominators.
2 3
2
6
12
t
6
18
1t 
2
3
t
2
3
Writing One-and Two-step Equations
An example:
Maggie is y years old. Kate is 15 years old. The total of Maggie and Kate’s ages equals 24. Write an equation that
you would use to find Maggie’s age.
By looking at this problem, you should know that if you add Maggie’s and Kate’s ages you would get 24.
Therefore, the equation you would write would be:
y + 15 = 24
Another example:
Charlie earns $6 for every hour that he works. He earned a total of $30. Write an equation that you would use to
find how many hours (h) he worked.
By looking at this problem, you should know that you would multiply the amount he earns per hour ($6)
by the number of hours he actually worked (h) to get his total pay ($30). Therefore, the equation you would write
would be: 6h = 30
Sometimes you have to do more than one operation in a problem.
Bobby hit the baseball 3 more than twice than number of times Paul hit it. Let p represent the number of times
Paul hit the baseball. What equation would you write to represent the number of times Bobby hit the baseball.
By looking at this problem, you know that first you must multiply the number of time Paul hit the baseball
(p) by 2. Then you must add 3 to this number. Your equation would be: 2p + 3
MA.7A.A.3.3 Practice Problems
1) -6x = -48
2) 3p + 7 = 25
4) 0.4z = -16
3)
y
= -3
8
5)
n
–2=5
4
6)
3
w = 18
5
7)
24 3
= a
16 4
8)
2
12
t=
5
25
9) World Connections long-distance phone company charges 15¢ per minute for each call. A customer receives a
$29.25 long-distance bill for last month’s calls. How many minutes of long-distance calls did she make?
10) Mauricio makes $350 per week plus $25 commission on each insurance policy he sells. Write and solve an
equation to determine how many policies he sold to earn $900.
11) For a warm up, Andrea runs 250 yards less than half the maximum distance she can run. This is represented
by the equation, r = ½ x – 250, were x represents the maximum distance run during her warm up. If Andrea ran
1,650 yards during her warm up on Tuesday, what is the maximum distance she can run?
A. 1,650 yards
B. 1,900 yards
C. 575 yards
D. 3,800 yards
2
x  4  10 ?
3
A. Add 4 to both sides of the equation, then multiply both sides by 2/3.
B. Add 4 to both sides of the equation, then multiply both sides by 3/2.
C. Subtract 4 from both sides of the equation, then multiply both sides by 2/3.
D. Subtract 4 from both sides of the equation, then multiply both sides by 3/2.
12. Which steps would solve
13. When Eric became a member of an exercise gym, he paid a one-time fee of $250. He then had to
pay $79.95 per month. So far, Eric has paid a total of $969.55, not including tax. What is the number of
months for which Eric paid?