Equations

Two equations are equivalent if they have exactly the same solutions.

3x = 6 is equivalent to x = 2

To solve an equation is to find the simplest equivalent equation that gives us the solution.

To obtain an equivalent equation we can do two basic operations only:

–Add or subtract the same expression in both sides of the equation.

–Multiply or divide by the same number (except zero) in both sides of the equality.

Example 1: To solve the equation 2 + x = 5

–We subtract 2 in both sides 2 + x – 2 = 5 – 2

–Then we obtain the solution x = 3

Example 2: To solve the equation 3x = 18

–We divide by 3 in both sides

Example 3: To solve the equation 2x + 5 = 9

–We subtract 5 in both sides 2x + 5 – 5 = 9 – 5

- We have 2x = 4 and we divide by 2

Maybe you will understand it better if you play with this weighing scales.

Example 4: To solve the equation x – 3 = -21

–We add 3 in both sides x – 3 + 3 = – 21 + 3

–Then we obtain the solution x = -18

Example 5: To solve the equation

–We multiply by 3 in both sides

You can practise a lot while playing in this webpage.

Exercise: solve these equations by using only the basic operations:

a) 2x - 5 = x + 7

b) 3x -2 = 2 (x - 1)

c) 2(x + 5) - (x + 3) = 3x - 6

Solutions: a) x = 12; b) x = 0; c) x = 13/2