**Solving Equations by Collecting Like Terms** *KS3 Revision*

## What you need to know

**Things to remember:**

- Before we can solve an equation we have to collect like terms.
- After collecting like terms we can solve as usual.

*Solve 5x + 2 -3x + 1=13*

We will solve this in 2 steps.

**Step 1: **Collect the like terms.

*Hint: **First try moving the terms that look similar next to each other, i.e. terms with letters and terms with just numbers.*

* *

5x + 2 -3x + 1=13

5x -3x+2 + 1=13

5x+3=13

*Step 2:** Solve the equation.*

*Hint: **Remember, we are doing BIDMAS in the opposite order and do opposite operations. Here we want to start by subtracting the 3.*

* *

5x+3=13

5x+3-3=13-3

5x=10

* *

*Hint: **After additions and subtractions we do multiplications and divisions. Here we need to divide by 5.*

5x=10

5x\div5=10\div5

x=2

*Solve -x+2+3-4+1-3x=-2*

We will solve this in 2 steps.

**Step 1: **Collect the like terms.

*Hint: **First try moving the terms that look similar next to each other, i.e. terms with letters and terms with just numbers.*

* *

-x+2+3-4+1-3x=-2

-x-3x+2+3-4+1=-2

-4x+2= -2

*Step 2:** Solve the equation.*

*Hint: **Remember, we are doing BIDMAS in the opposite order and do opposite operations. Here we want to start by subtracting the 2.*

-4x+2= -2

-4x+2-2= -2-2

-4x= -4

* *

*Hint: **After additions and subtractions we do multiplications and divisions. Here we need to divide by -4.*

*Hint: **Remember, when we divide by a negative number it changes the sign.*

*Negative divided by a negative equals a positive.**Positive divided by a negative equals a negative*

* *

-4x= -4

-4x\div-4= -4\div-4

x=1

## Example Questions

**Question 1:** *Solve 7y+2-3+y=23*

**Step 1: **Collect the like terms.

*Hint: **First try moving the terms that look similar next to each other, i.e. terms with letters and terms with just numbers.*

* *

7y+2-3+y=23

7y+y+2-3=23

8y-1=23

*Step 2:** Solve the equation.*

*Hint: **Remember, we are doing BIDMAS in the opposite order and do opposite operations. Here we want to start by adding the 1.*

* *

8y-1=23

8y-1+1=23+1

8y=24

* *

*Hint: **After additions and subtractions we do multiplications and divisions. Here we need to divide by 8.*

* *

8y=24

8y\div8=24\div8

y=3

**Question 2:** *Solve 5-4z-3+2-5z=-59*

**Step 1: **Collect the like terms.

*Hint: *

* *

5-4z-3+2-5z=-59

-4z-5z+5-3+2=-59

-9z+4=-59

*Step 2:** Solve the equation.*

*Hint: **Remember, we are doing BIDMAS in the opposite order and do opposite operations. Here we want to start by subtracting the 4.*

* *

-9z+4=-59

-9z+4-4=-59-4

-9z=-63

* *

*Hint: **After additions and subtractions we do multiplications and divisions. Here we need to divide by -9.*

*Hint: **Remember, when we divide by a negative number it changes the sign.*

*Negative divided by a negative equals a positive.*

*Positive divided by a negative equals a negative*

* *

-9z=-63

-9z\div-9=-63\div-9

z=7