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SQA National 5 Maths Linear equations

Linear equations

This page covers the following topics:

1. Solving linear equations
2. Linear equations with brackets
3. Equivalent expressions

To find the unknown in a linear equation the balancing method can be used. In the balancing method we either add or subtract the same value on each side of the equation so that only the unknown is left on one side of the equal sign.

Solving linear equations

To solve a linear equation that contains a set of brackets first use the balance method to ensure that the brackets are alone on one side of the equation. Then divide the whole equation by the value in front of the brackets and then use the balance method to solve the rest of the equation.

Linear equations with brackets

If two expressions can be rearranged to be exactly the same, they are called equivalent expressions. Various operations can be used to prove or check that two expressions are equivalent, including balancing method, expanding brackets and factorisation.

Equivalent expressions

1

Solve βˆ’3(w + 7) βˆ’ 7 = w/2 βˆ’ 49/2.

Solve βˆ’3(w + 7) βˆ’ 7 = w/2 βˆ’ 49/2.

2

Are expressions 3x + 1 βˆ’ 7x and 6 βˆ’4x βˆ’ 5 equivalent? Show your working.

Are expressions 3x + 1 βˆ’ 7x and 6 βˆ’4x βˆ’ 5 equivalent? Show your working.

3

Solve equation 4(x + 2) + 5 = 17.

Solve equation 4(x + 2) + 5 = 17.

4

Prove that the expressions 2(x + 5) + 2 βˆ’ 16x and 3(x βˆ’ 1) βˆ’ 17x + 15 are equivalent.

Prove that the expressions 2(x + 5) + 2 βˆ’ 16x and 3(x βˆ’ 1) βˆ’ 17x + 15 are equivalent.

5

Volume of a tin of beans is 2 units less than the volume of a milk pack. Create an equation that relates these two volumes and find the value of z.

Volume of a tin of beans is 2 units less than the volume of a milk pack. Create an equation that relates these two volumes and find the value of z.

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