Solving Equations by Collecting Like Terms | KS3 Maths Resources

## 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

$$-4x= -4$$

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

$$x=1$$

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## Example Questions

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.

$$8y=24$$

$$8y\div8=24\div8$$

$$y=3$$

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.

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

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

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

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

$$-9z=-63$$

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

$$z=7$$

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