One-Step Equations
x + 12 = 0
x = - 12
6x – 13 = 11
x = 4
4x + 3 = 7
x = 1
What are equivalent equations?
Equivalent equations are algebraic equations that have identical solutions.
Fractions represent this operation.
Division
The product of q and - 6 is 30
-6q = 30
4 = - 8 + x
x = 12
7(2z+1)=35
z = 2
4 + 5x = 29
x = 5
What would be your first step to solve 5x + 2 = 10?
Subtract 2 from both sides.
When solving a two step equation how many terms are usually on the same side?
Two
Two thirds of a number, m, gives a result of 12.
2/3m = 12
3 = - 2 – x
x = - 5
x/2 + 13 =-8
x= - 42
3/8p-1/6=3/4p-3/4
p=1 5/9 or 1.5
What would be your first step to solve
(2x + 1)/2 =6
Multiply both sides by 2.
How does an equation differ from an expression?
An equation involves two sets of equal terms. An expression is just a series of terms.
A number, k, is tripled and then 4 is added. The result is halved to obtain -13.
(3k + 4)/2 = -13
5/2y+8=18
y=4
1.4z-0.5 =3.7
x = 3
14 = (3a + 6) + 2
a = 2
Are these equations equivalent?
x + 2 = 7 and 2x + 1 = 11
YES
You are given an equation with pronumerals on both sides. What is your first step in solving the equation?
move a pronumeral term from one side.
The average of 3x and 10 is 14.
(3x + 10)/2 = 14
-1/8 = x + 2
x=-2 1/8
x/3 - 6 = -3
x = 9
5(u+1)=3(3u+4)
u=-7/4
Are these equations equivalent?
2x + 4 = 20 and 2x + 7 = 23
YES
Describe two methods for solving equations with brackets.
Division method: Divide both sides by the term before the brackets first to remove brackets.
Expanding method: multiply the term before the brackets by the terms within the brackets to remove brackets.
Maddie's age 8 years ago when multiplied by 5 is the same a triple Maddie's age in 2 years time.
5(m - 8) = 3(m + 2)
(m = 32)