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Level 5-6 Algebra - Equations with Letters on Both Sides
Think before you answer each question.

Level 5-6 Algebra - Equations with Letters on Both Sides

In your KS3 Maths journey, algebra is a part you'll spend a lot of time tackling. Sometimes, you'll face equations with letters on both sides of the equals sign, and that's what this quiz is all about. Remember the handy rule: 'change sides, change signs,' and you'll be on the right track.

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To make things easier, try the 'cover-up' method. For instance, in 3x + 4 = 10, cover up the x-term and replace it with 'what.' So, 'what plus 4 equals 10?' Easy, right? The answer is 6. Move on to the next line, which becomes 3x = 6. Finally, it leads to x = 2. A bit trickier when the variable is on both sides, but you'll get the hang of it!

This quiz is perfect practice for solving equations with letters on both sides. You'll be a pro by the time you finish!

1.
What is the value of d in the following equation: 13d + 8 = 7d + 3d + 35?
7
9
11
13
'Write it down and work it out'. There is no alternative to a step by step approach!
2.
What is the value of e in the following equation: 2(e + 5) = 44?
0.7
7
17
27
2(e + 5) = 44 is the same as 2e + 10 = 44 so 2e = 34. 34 divided by 2 = 17
3.
4(a + 7) = 40 is the same as which of the following?
4 - a - 7 = 40
4 - a + 7 = 40
4 + a + 7 = 40
4a + 28 = 40
Multiply the 4 (outside of the brackets) with both the a and the 7 (inside the brackets)
4.
What is the value of f in the following equation: 7(f - 5) = 4(f - 3.5)?
7
9
11
13
7(f - 5) = 4(f - 3.5) is the same as 7f - 35 = 4f - 14. f must equal 7
5.
Look at the equation 4(a - 4) = 3a - 9. Now decide which of the following is not correct.
4a - 16 = 3a - 9
a = -9 + 16
a = 7
a = 25
Simplifying equations makes them a lot easier to solve
6.
Look at this equation: 10x + 18x = 7x + 189. Now decide which of the following is not correct.
10x + 18x + 7x = 189
10x + 18x - 7x = 189
21x = 189
x = 9
When we rewrite the equation as 10x + 18x - 7x = 189, we've moved the 7x from one side of the equals sign to the other. That means that it changes from a positive to a negative number
7.
Look at this equation: 10 + 18 = 7x. Now decide which of the following is not correct.
7x = 10 + 18
7x = 10 - 18
7x = 28
x = 4
First get the letter x onto the left hand side and then, in stages, break down its value
8.
What is the value of c in the following equation: 4c = 2c + 75?
8
37.5
75
150
2c = 75
9.
2x + 3y = 3y + 7 is the same as which of the following?
2x = 6y + 7
2x = 7
y = 2x - 7
y = 2x + 7
When + 3y crosses over to the other side it becomes - 3y and cancels out the 3y that was already on that side
10.
x + 7 = 10 + 12 is the same as which of the following?
x = 10 + 12 - 7
x = 10 + 12 + 7
x = 17 + 19
x = 70 + 84
When the 7 crosses over to the other side it becomes - 7
You can find more about this topic by visiting BBC Bitesize - Equations

Author:  Frank Evans
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