XX22 + 2 = 11 + 2 = 11

XX2 2 = 9= 9

X = 3

Check: X2 + 2 =

3 x 3 +2 = 11

We can solve this equation by:

XX22 + 2 = 15 + 2 = 15

This is a method where we substitute different values for x until we get as close as we can to the answer, usually one decimal place

Look at this equation:

We can solve this in a similar way but for this type we are often asked to use

trial and improvement

Using trial and improvement Using trial and improvement show that the equationshow that the equation

X X22 + 2 = 15 + 2 = 15 has a solution between 3 and 4has a solution between 3 and 4

The first thing we do is set up a The first thing we do is set up a table of valuestable of values

GuessGuess XX22 + 2 = 15 + 2 = 15 CommentComment

In this column we write our guess or estimate

Write the equation here

Is the answer too big or too small?

GuessGuess XX22 + 2 = 15 + 2 = 15 CommentComment

3 11 Too small

4 18 Too big

3.5 14.25 Too small

Try a value half- way between 3 and 4

Too small3.6 14.96

3.7 15.69 Too bigTo decide if the solution is closer to 3.6 or 3.7, try the middle value3.653.65 15.3225 Too big

The solution is between 3.6 and 3.7 we cannot just guess which is closer

Always write down all the digits on your calculator

We only need the answer correct to one We only need the answer correct to one decimal placedecimal place

X = 3.65 was too big.X = 3.65 was too big. So your next guess would be smallerSo your next guess would be smaller So you could try 3.64 or 3.63So you could try 3.64 or 3.63 All these are 3.6 correct to 1 decimal placeAll these are 3.6 correct to 1 decimal place

3.63.65 3.7

So correct to one decimal place x would equal 3.6

Using trial and improvement Using trial and improvement show that the equationshow that the equation

X X33 + 2x = 7 + 2x = 7 has a solution between 1 and 2has a solution between 1 and 2

The first thing we do is set up a The first thing we do is set up a table of valuestable of values

GuessGuess XX33 + 2x = 7 + 2x = 7 CommentComment

In this column we write our guess or estimate

Write the equation here

Is the answer too big or too small?

GuessGuess XX33 + 2x= 7 + 2x= 7 CommentComment

1 3 Too small

2 12 Too big

1.5 6.375 Too small

Try the value half- way between 1 and 2

Too big1.6

7.296

1.55 6.823875 Too small

To decide if the solution is closer to 1.5 or 1.6, try the middle value

1.55

The solution is between 1.5 and 1.6 remember we cannot just guess which is closer

We only need the answer correct to one We only need the answer correct to one decimal placedecimal place

X = 1.55 was too small.X = 1.55 was too small. So your next guess would be biggerSo your next guess would be bigger You could try 1.56 or 1.57You could try 1.56 or 1.57 All these would be 1.6 correct to 1 decimal All these would be 1.6 correct to 1 decimal

placeplace

1.51.55 1.6

So correct to one decimal place x would equal 1.6

Using trial and improvement Using trial and improvement show that the equationshow that the equation

X X33 + x = 105 + x = 105 has a solution between 4 and 5has a solution between 4 and 5

Set up a table of valuesSet up a table of values

GuessGuess XX33 + x = 105 + x = 105 CommentComment

GuessGuess XX33 + x = + x = 105105

CommentComment

4 68 Too small

5 130 Too big

4.5 95.625 Too smallTry the value half- way between 4 and 5

Too small4.6 101.936

4.7 108.523 Too big

To decide if the solution is closer to 4.6 or 4.7, try the middle value

4.654.65 105.194625 Too big

The solution is between 4.6 and 4.7. Remember, we cannot just guess which is closer

We only need the answer correct to one We only need the answer correct to one decimal placedecimal place

X = 4.65 was too big.X = 4.65 was too big. So your next guess would be smallerSo your next guess would be smaller You could try 4.64 or 4.63You could try 4.64 or 4.63 All these would be 4.6 correct to 1 decimal All these would be 4.6 correct to 1 decimal

placeplace

4.64.65 4.7

So correct to one decimal place x would equal 4.6

Using trial and improvement Using trial and improvement show that the equationshow that the equation

3X 3X22 - 4x = 18 - 4x = 18 has a solution between 3 and 4has a solution between 3 and 4

Set up your table of valuesSet up your table of values

GuessGuess 3X3X22 - 4x = 18 - 4x = 18 CommentComment

GuessGuess 3X3X22 - 4x= - 4x= 1818

CommentComment

3 15 Too small

4 32 Too big

3.5 22.75 Too big

Try the value half- way between 3 and 4

Too big3.4 21.08

3.3 19.47 Too big

To decide if the solution is closer to 3.2 or 3.3, try the middle value

3.25The solution is between 3.2 and 3.3 remember, we cannot just guess which is closer

3.2 17.92 Too small

3.25 18.6875 Too big

Remember to write down all the digits on your calculator

We only need the answer correct to one We only need the answer correct to one decimal placedecimal place

X = 3.25 was too big.X = 3.25 was too big. So your next guess would be smallerSo your next guess would be smaller So you could try 3.24 or 3.23So you could try 3.24 or 3.23 All these would be 3.2 correct to 1 decimal All these would be 3.2 correct to 1 decimal

placeplace

3.23.25 3.3

So correct to one decimal place x would equal 3.2