# 1819 G2X §9.2

Which exercises should we discuss on the board?
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Slide 1: Mind map
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 10 slides, with interactive quizzes and text slides. Lesson duration is: 50 min

## Items in this lesson

Which exercises should we discuss on the board?

#### Slide 1 -Mind map

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

#### Slide 2 -Open question

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.

#### Slide 3 -Slide

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.

#### Slide 4 -Slide

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

#### Slide 5 -Slide

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!

#### Slide 6 -Slide

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)

#### Slide 7 -Slide

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.

#### Slide 8 -Slide

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 =

31

#### Slide 9 -Slide

HW Friday
Make and correct §9.2