Page 102 - MAT KS3 Y8 Cambridge CheckPoint

9.3 Constructing and solving equations

2 Work out the value of x in each of these isosceles triangles. All measurements are in centimetres.
a b c
6x – 3 9 x + 35 5x – 13
27 3(x + 5)

3 Work out the value of y in each of these shapes. All measurements are in centimetres.
a b 8y – 5 c
2(y + 6) 4(y – 3)
4(y – 3) 2y + 2

3(y + 5)

4 Work in a group of three or four. For each part of this question:
i write down an equation to represent the problem
ii compare the equation you have written with the equations written by the other members of your
group and decide who has written the correct equation in the easiest way
iii solve the equation that you chose in part ii.
a Xavier thinks of a number. He multiplies it by 3 then adds 8. The answer is 23. What number
did he think of?
b Anders thinks of a number. He divides it by 4 then subtracts 8. The answer is 5. What number
did he think of?
c Sasha thinks of a number. She multiplies it by 5 then subtracts 4. The answer is the same as
2 times the number plus 20. What number did Sasha think of?
d Alicia thinks of a number. She multiplies it by 3 then adds 7. The answer is the same as 4 times
the number. What number did Alicia think of?
e Jake thinks of a number. He adds 5 then multiplies the result by 2. The answer is the same as
5 times the number take away 14. What number did Jake think of?
f Harsha thinks of a number. She subtracts 2 then multiplies the result by 3. The answer is the
same as subtracting 6 from the number then multiplying by 7. What number did Harsha
think of?

Summary
You should now know that: You should be able to:
★ When you simplify or transform an expression you ★ Simplify, or transform, linear expressions with
must make sure you don’t change the value or the integer coefficients.
meaning of the expression. ★ Collect like terms.
★ You can simplify expressions by collecting like ★ Multiply a single term over brackets.
terms.
★ Construct and solve linear equations with integer
★ When you multiply out, or expand, brackets, you coefficients (unknown on either or both sides,
multiply each term inside the brackets by the term with or without brackets).
outside the brackets.
★ When you are given a problem to solve, you may
need to construct or write an equation to help you
solve the problem.

100 9 Simplifying expressions and solving equations