Chapter 2 – Equations
Learning Targets:
I can:




Solve one-step equations 2.1
Solve two-step equations 2.2
Solve multi-step equations 2.3
Solve proportions 2.6
One-step equations –
x + 3 = 8… When solving these equations, there are some properties that we have to know:
Addition Property of Equality – Adding the same number to both sides of an equation, and the
statement will still be true. 3 = 3 3 + 2 = 3 + 2. Algebra: a = b a + c = b + c
Subtraction Property of Equality – Subtracting the same number to both sides of an equation, and the
statement will still be true. 7 = 7 7 – 5 = 7 – 5. Algebra: a = b a – c = b – c
Multiplication Property of Equality – Multiplying both sides of an equation by the same number, and the
statement will still be true. 6 = 6 6(3) = 6(3). Algebra: a = b ac = ac
Division Property of Equality – Dividing both sides of an equation by the same nonzero number, and the
statement will still be true. 8 = 8
8
4
8
= 4. Algebra: a = b (c ≠ 0)
𝑎
𝑐
𝑏
=𝑐
In order to decide which property to use, choose the opposite sign that you see:
X – 3 = 4 = Addition property of equality
X + 4 = 4 = Subtraction property of equality
𝑥
3
= 12 = Multiplication property of equality
4x = 12 = Division property of equality
For each equation, you are trying to solve for the variable (letter). You must get the variable by itself to
determine the answer.
Two – Step Equations
The same properties in the one-step equations apply. The difference is, we have two steps instead of
one. For the typical two-step equations, your goal is to still get the variable by itself, but first, we need
to get the constants on one side of the equal sign.
Example:
2x – 6 = 4
This equation has a coefficient (2), a variable (x), a constant (-6) , equal sign (= ) a constant (4)
We do not want a constant on each side of the equal sign, so we need to use the addition property of
equality to move the 6 to the other side:
2x – 6 = 4
+6 +6
The 6 on the left side is removed and added to the right. We’re left with 2x = 10. What’s next? The
division property of equality
Step 1 – Move the constant
Step 2 – Divide to get the variable by itself.
Exception:
X+3=5
4
For this equation, we must remove the denominator. To do that, we must apply the Multiplication
property of equality. Then, use the subtraction property of equality to get the variable by itself.
Multi-Step Equations
5(x + 2) = -3x
5(x + 2) is a distributive property. This means that everything inside the parenthesis is multiplied by the
5.
Another way of looking at distributive property is:
(x + 2) +( x + 2) +( x + 2) + (x + 2) + (x + 2) if we add the like terms, we will get 5x + 10
Rewrite the equation:
5x + 10 = 3x
Next, move the variables so that they are on the same side by applying the subtraction property of
equality
5x – 5x + 10 = 3x – 5x
10 = -2x Next apply the division property of equality to get x by itself.