**Solving two step equations : **

In this section, we are to see how two-step equations can be solved.

We can use inverse operations to solve equations with more than one operation.

**Example 1 : **

Five less than the quotient of a number and 4 is 15. What is the number ?

**Solution : **

**Step 1 :**

Let n represent the number. Write an equation.

n/4 - 5 = 15

**Step 2 : **

n/4 - 5 = 15

Add 5 to both sides

(n/4 - 5) + 5 = 15 + 5

n/4 = 20

Multiply both sides by 4

4.(n/4) = 4.(20)

n = 80

Hence, the number is 80.

**Example 2 : **

The Wilsons have triplets and another child who is ten years old. The sum of the ages of their children is 37. How old are the triplets ?

**Solution : **

**Step 1 :**

Let m represent the age of each child in triplet. Write an equation.

3m + 10 = 37

**Step 2 : **

3m + 10 = 37

Subtract 10 on both sides

(3m + 10) - 10 = 37 - 10

3m = 27

Divide both sides by 3

3m/3 = 27/3

m = 9

Hence, the age of each child in the triplet is 9 years.

**Example 3 : **

A dog sled driver added more gear to the sled, doubling its weight. This felt too heavy, so the driver removed 20 pounds to reach the final weight of 180 pounds. Write and solve an equation to find the sled’s original weight.

**Solution : **

**Step 1 :**

Let w represent the original weight of the sled. Write an equation.

2w - 20 = 180

**Step 2 : **

2w - 20 = 180

Add 20 to both sides

(2w - 20) + 20 = 180 + 20

2w = 200

Divide both sides by 2

2w/2 = 200/2

w = 100

Hence, the sled’s original weight was 100 pounds.

In this section, we are going to see, how two-step equations can be solved using modeling.

We will be using the following algebra tiles to model and solve two-step equations.

**Example 1 : **

Use algebra tiles to model and solve 3n + 2 = 11.

**Solution : **

**Step 1 :**

How can we model the left side of the equation ?

We find 3n + 2 on the left side of the equation. So we can use three positive variable tiles and two +1 tiles to model the left side of the equation.

**Step 2 : **

How can we model the right side of the equation ?

We find positive 11 on the right side of the equation. So we can use eleven +1 tiles to model the right side of the equation.

**Step 3 : **

Now use the above mentioned algebra tiles or draw them to model the equation on the mat.

**Step 4 : **

Remove two +1 tiles from each side of the mat.

**Step 5 : **

Divide each side into 3 equal groups.

**Step 6 : **

The solution is n = 3.

**Example 2 : **

Use algebra tiles to model 2x - 3 = 5.

**Solution : **

**Step 1 :**

How can we model the left side of the equation ?

We find 2x - 3 on the left side of the equation. So we can use two positive variable tiles and three -1-tiles to model the left side of the equation.

**Step 2 :**

How can we model the right side of the equation ?

We find positive 5 on the right side of the equation. So we can use five +1 tiles to model the right side of the equation.

**Step 3 : **

Now use the above mentioned algebra tiles or draw them to model the equation on the mat.

**Step 4 : **

Add three +1 tiles on each side of the mat.

**Step 5 : **

Identify and remove zero pairs on each side of the mat.

**Step 6 : **

Divide each side into 2 equal groups.

**Step 7 : **

The solution is x = 4.

After having gone through the stuff given above, we hope that the students would have understood "Solving two step equations".

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