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

Answer

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

Answer

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