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Home > Maths I > Relationships > Simple equations and inequalities

Maths I

Simple equations and inequalities

Solving equations (continued)

Have a look at these examples:

Example 1

Solve 3x = x + 10

With this type of equation put all the x terms on the left hand side.

If we 'take away' the x term from the right hand side, we must do exactly the same thing to the left hand side to keep the equation balanced.

A balanced pair of weighing scales. On one side the weight says 3x. On the other side the weight says x plus 10.

3x - x = x + 10 - x

Weighing Balance (3x - x = x + 10 - x)

So 2x = 10

Therefore x = 5 is the solution.

Example 2

Solve 3y + 1 = 2y + 7

Put all the y terms on the left.

So, take 2y away from the right hand side and also away from the left hand side (to keep the equation balanced).

A balanced weighing scale. On one side the weight says 3 y plus 1, and on the other side it says 2 y plus 7.

3y + 1 - 2y = 2y + 7 - 2y

Weighing Balance (3y + 1 - 2y = 2y + 7 - 2y)

So y + 1 = 7

Therefore y = 6 is the solution.

Example 3

Solve 5a - 3 = 3a + 4

A baalnced pair of weights on a scale. On one side the weight says 5 a minus 3. On the other side the weight says 3 a plus 4.

5a - 3 - 3a = 3a + 4 - 3a

Weighing Balance (5a - 3 - 3a = 3a + 4 - 3a)

2a - 3 = 4

2a = 7 (because 7 - 3 = 4)

Therefore a = \frac{7}{2} is the solution.

Now try to solve these equations.

Question

Solve 5y = 3y + 12

Answer

\;y = 6 (because 2y = 12)

Question

Solve 2x + 5 = x + 8

Answer

x = 3 (because x + 5 = 8)

Question

Solve 4m + 2 = 2m + 9.

Answer

m = \frac{7}{2}

This is because

2m + 2 = 9, 2m = 7).

Question

Solve 7x - 12 = 3x + 10.

Answer

x = \frac{22}{4} or \frac{11}{2}

This is because

4x - 12 = 10, 4x = 22).

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