Linear Equations

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Lineair equations

Goal: How to solve all kinds of lineair equations?

Solve.

3x+5=11

3x+5=11

1. x=5​3​​1​​
2. x=3
3. x=2
4. x=18

Answer A

3x+5=11

3x=16

x=​3​​16​​=5​3​​1​​

Answer B

3x+5=11

3x=6

x=3

Answer D

3x+5=11

3x=6

x=18

Answer C

3x+5=11

3x=6

x=2

In the following exercises you need to spot a possible mistake in a step by step solution.

Which step contains a mistake? There may be no mistake.

step 1

step 2

step 3

5x−7=−3x+4

8x−7=4

8x=−3

x=−​8​​3​​

Which step contains a mistake?

step 1
step 2
step 3

5x−7=−3x+4

8x−7=4

8x=−3

x=−​8​​3​​

1. Step 1
2. Step 2
3. Step 3
4. No mistakes

Which step contains a mistake? There may be no mistake.

step 1

step 2

step 3

5x−7=−3x+4

8x−7=4

8x=−3

x=−​8​​3​​

4−2x=5x−8

4−7x=−8

−7x=−12

x=1​7​​5​​

Which step contains a mistake? There may be no mistake.

step 1

step 2

step 3

Which step contains a mistake?

step 1
step 2
step 3

4−2x=5x−8

4−7x=−8

−7x=−12

−7x=−12

−7x=−12

x=1​7​​5​​

−7x=−12

−7x=−12

x=1​7​​5​​

1. Step 1
2. Step 2
3. Step 3
4. No mistakes

4−2x=5x−8

4−7x=−8

−7x=−12

x=1​7​​5​​

Which step contains a mistake? There may be no mistake.

step 1

step 2

step 3

How to solve an equation:
(Write this down.)

1. Multiply out brackets
2. Simplify both side
   and get rid of fractions
3. Move all terms with x to lhs and all the others to rhs
4. Divide by the number before x.
   

​3​​2​​(4x+12)=​6​​1​​(8x−9)

Practice

• Make exercise 7 on page 12
• you have 7 minutes.
• Work alone
• Finished? Great, make a start on ex. 8
• at the end of the time, tell me how you did
  

'B-subject'

• a subject you're more likely to use in math B
• warning: may also be needed for math A
• will be on tests
  

​4​​3+x​​+​3​​x−8​​=2

Strange results

0x=4

0x=0

Problem: We cannot divide by zero.

Which is a solution to:

0x=4

1. x=4
2. x=​4​​1​​
3. x=0
4. No solutions

0x=4

No solutions.

Which is a solution to:

0x=0

1. x=4
2. x=​4​​1​​
3. x=0
4. No solutions

0x=0

Every value of x is a solution.

Homework

Make exercises 7, 8, 10, 11