Solving Equations

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

What is this Chapter about?

In this chapter we will look at ways in which you can solve equations. 

You need to identify what type of equation so that you can decide which method to use.

How well have you understood this chapter?

We will now solve some equations to see how well you have understood the explanation. Maybe you don't know how to solve all of the types of equation and need extra explanation.

Solve equation a)
What is your solution?
x=?

Solve equation b)
What is your solution?
x=?

Solve equation c)
What is your solution?
x=?

Solve equation d)
What is your solution?
x=?

Solve equation e)
What is your solution?
x=?

Solve equation f)
What is your solution?
x=?

All answers correct or only one mistake

You have understood the basis of the chapter .

Now you can practise questions with more text .

ex 32 t/m 38 on pages 88 & 89

You made two mistakes 

Maybe you were just unlucky so try some more and see if you do any better this time.

T7 & T8 on page 93

ex 35, 37 and 38 on page 89

More than two mistakes

Never mind! 

With a bit more explanation you will do better next time!

Please pay attention.

Solving an equation using cards

6k+12=30

Think carefully where the card should be placed.

Work out what number should be written on the card?

What is k equal to?

"expressed in terms of"

In the formula y=4x+7 We say y is"expressed in terms of" x

Sometimes you need to re-arrange the formula to get it expressed in this way.

eg. 6q + 12p = -18

6q = -18 -12p    and dividing by 6 gives

q = -3 -2p

Simultaneous equations

You can solve simultaneous equations 

by first re-arranging the formulas and then putting them equal to each other so that you have an equation to solve.

y=3x+7

y+4x=0    becomes  y = -4x

so 3x+7 = -4x

7x = -7  so x = -1

or 

by substituting

y=x-1 and 4y+ x = 16 so gives 4(x-1)+x = 16

4x-4+x=16  which is 5x=20 so x=4

Fractional equations

Using Cards

18/(2x+1) =2

so 2x+1 = 9 so 2x=8   x=4

However if there are variables on both sides of the equation, multiply both sides by the denominator of the fraction.

(x+7) = -9/(x-3)

(x-3)(x+7) = -9 you can now solve giving x=-6 or x=2

Exponential equations

These are equations like:

To solve these you need to write the number also as a power

square root equations

Square both sides to remove the square root. Or use cards.

Then you can solve in the usual way.

power equations

These are equations that contain a power of the variable.

Now you are ready to try again!

T1,  T2 a,b,c   , T3, T4, T5 a,b,c  , T6 a,b,c

and

ex 36  on page 89

Homework: Finish your exercises and check your answers.

If you have any questions put a ? in the margin next to the question and ask me about it next lesson.