Solving One-step Equations Algebraically

The goal of solving equations: -To get one x alone on one side of the equation.

The rule for solving equations: -Do the same thing to both sides of the equation.

• Today, we will connect modeling equations with algebra tiles to solving equations algebraically.

• Our goal and rule for solving equations, however, have not changed.

Let’s start with an addition equation… x + 2 = 7

To get x alone, take 2 units from each side.

In math, “take away” means to subtract.

x + 2 = 7

X = 5

With algebra tiles Algebraically

x + 2 = 7- 2 - 2

x = 5

Think opposite operations: To undo “x plus 2,” we subtracted 2.

Let’s try a multiplication equation… 3x = 15

3x = 15

X = 5

With algebra tiles Algebraically

3x = 15 To get x alone, split both sides into 3 groups.

In math, “splitting into groups” means to divide.

3 3

x = 5

Think opposite operations: To undo “3 times x,” we divided by 3.

Now for a subtraction equation… x – 3 = 8

With algebra tiles Algebraically

x – 3 = 8 To get x alone, add 3 units to both sides.

In math, “adding 3 ” means + 3.

+ 3 + 3

x = 11

Think opposite operations: To undo “x minus 3,” we added 3.

X = 11

x – 3 = 8

x + -3 = 8

We did not model a division equation. Based on the previous examples, can you guess what will happen?

How will we “undo” division?

Algebraically

We will use multiplication to “undo” division.

In this case, we will multiply both sides by 5.

(5) (5)

x = 20

Think opposite operations: To undo “x divided by 5,” we multiplied by 5.

45

x