ALG; 2-3: Solving Two-Step and Multi-Step Equations
Vocabulary
Null or Empty Set: Equations that have No Solution.
Identity: Equations with an Infinite number of solutions.
Steps in Solving
To solve Two-Step Equations…
I. Undo/cancel all addition and subtraction operations FIRST.
II. Undo/cancel all multiplication and division operations SECOND.
Similarly to using inverse operations when canceling out… you also use the inverse order of operations when solving an equation.
Example
10 = 6 – 2x
Problems/Examples of
A)
– 4 + 7x = 34
B) 1.5 = 1.2y – 5.7
C)
n
22
7
You should always check your solutions to equations, by substituting your solution back into the original equation to see if the equation is true.
To solve Equations that contain Fractions…
I. Write an equivalent equation with common denominators in ALL terms.
II. Once all the terms have common denominators, you can cancel all the denominators and solve the equation normally.
Example
q 1 3
 
15 5 5
Problems/Examples of
D)
2x 1
 5
5 2
E)
3
1 7
u 
4
2 8
F)
1
1 8
n 
5
3 3
You should always check your solutions to equations, by substituting your solution back into the original equation to see if the equation is true.
To solve a multi-step equation that contains grouping symbols…
I.
If necessary…simplify the equation by clearing out all parentheses using the Distributive Property.
II.
Continue simplifying the equation by Combining Like Terms (Use inverse operations; if like terms are on opposite sides of the
equal sign.
III.
Solve the equation using inverse operations.
Example
3h = 5(h - 2)
Problems/Examples of
G)
6(b – 2) = 3(b + 8.5)
H)
6x + 3 – 8x = 13
I)
9 = 6 – (x + 2)
You should always check your solutions to equations, by substituting your solution back into the original equation to see if the equation is true.
Solve each equation. Check your solutions.
J)
2a + 3 – 8a = 8
K)
-2(3 – d) = 4
L) 4(x – 2) + 2x = 40
Solve the equation, and then use your solution to find the indicated value.
If 3a + 12 =30;
Find the value of a + 4.
M) If 2x + 4 = -24;
Find the value of 3x.
N) If 5(y – 2) = 30;
Find the value of ¼ y.
O) If 4 – 3b = 19;
Find the value of -2b
Write an equation to represent each relationship. Solve each equation.
P) The difference of 11 and 4 times a number equals 3.
Equation: _____________________
Q) Thirteen less than 5 times a number is equal to 7.
Equation: _____________________
R) Alex belongs to a music club. In this club, students can buy a S) Sara paid $15.95 to become a member at a gym. She then
student discount card for $19.95. This card allows them to buy
paid a monthly membership fee. Her total cost for 12months was
CDs for $3.95 each. After one year, Alex has spent $63.40.
$735.95. How much was the monthly fee?
Write and solve an equation to find how many CDs Alex bought
during the year.
Equation: _______________________
Equation: _______________________
Write and solve an equation to find the value of x for each triangle. (Hint: The sum of the angle measures in any triangle is 180o.)
T)
Equation: __________________________