1819 G2X §9.2

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• Middelbare school
• havo, vwo
• Leerjaar 2

Which exercises should we discuss on the board?

Solve 8a + 3 = 3a + 13
(show steps!)

Solving equations

You can solve 8a + 3 = 3a + 13 with the balance method.

First your subtract 3a from both sides:       5a + 3 = 13

Then your subtract 3 from both sides:        5a = 10

Then divide by 5 on both sides:                         a = 2

So far we have seen positive, whole solutions.

Solving equations

The balance method can also be used with negative numbers, fractions and decimal numbers.

We keep following the rules of the balance method:

- You can add or subtract the same term from both sides of the equal sign.

- You can multiply or divide by the same number on both sides of the equal sign.

Examples

Solve:                                                      2a + 5 = 19 - 5a

+ 5a on both sides:                           7a + 5 = 19

- 5 on both sides:                               7a = 14

÷ 7 on both sides:                               a = 2

Examples

Solve:                                                      -3r - 4 = 2r + 7

- 2r on both sides:                           -5r - 4 = 7

+ 4 on both sides:                             -5r = 11

÷ -5 on both sides:                           r = -2.2

We can also solve the same equation in a different way!

Examples

Solve:                                                      -3r - 4 = 2r + 7

+ 3r on both sides:                            - 4 = 5r + 7

- 7 on both sides:                               -11 = 5r

÷ 5 on both sides:                               -2.2 = r

(It is common to then also write the solution as r = -2.2)

Equations with brackets

If you want to solve          2(3t - 4) = -3(5t - 2) - 7

you must first remove the brackets and write each side of the equation as short as possible, before you can use the balance method.

Equations with brackets

Solve:                                                 2(3t - 4) = -3(5t - 2) - 7

Remove brackets:                        6t - 8 = -15t - 1

+ 15t on both sides:                     21t - 8 = -1

+ 8 on both sides:                         21t = 7

÷ 21 on both sides:                        t =

​3​​1​​

HW Friday

Make and correct §9.2