X = 11 X 2 = 9 X = 3 Check: X = 3 x 3 +2 = 11 We can solve this equation by:

X = 15 X = 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 show that the equation X = 15 has a solution between 3 and 4 The first thing we do is set up a table of values

Guess X = 15 Comment In this column we write our guess or estimate Write the equation here Is the answer too big or too small?

Guess X = 15 Comment 311 Too small 418 Too big Too small Try a value half- way between 3 and 4 Too small Too big To decide if the solution is closer to 3.6 or 3.7, try the middle value 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 decimal place We only need the answer correct to one decimal place X = 3.65 was too big. X = 3.65 was too big. So your next guess would be smaller So your next guess would be smaller So you could try 3.64 or 3.63 So you could try 3.64 or 3.63 All these are 3.6 correct to 1 decimal place All these are 3.6 correct to 1 decimal place So correct to one decimal place x would equal 3.6

Using trial and improvement show that the equation X 3 + 2x = 7 has a solution between 1 and 2 The first thing we do is set up a table of values

Guess X 3 + 2x = 7 Comment In this column we write our guess or estimate Write the equation here Is the answer too big or too small?

Guess X 3 + 2x= 7 Comment 13 Too small 212 Too big Too small Try the value half- way between 1 and 2 Too big 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 decimal place We only need the answer correct to one decimal place X = 1.55 was too small. X = 1.55 was too small. So your next guess would be bigger So your next guess would be bigger You could try 1.56 or 1.57 You could try 1.56 or 1.57 All these would be 1.6 correct to 1 decimal place All these would be 1.6 correct to 1 decimal place So correct to one decimal place x would equal 1.6

Using trial and improvement show that the equation X 3 + x = 105 has a solution between 4 and 5 Set up a table of values

Guess X 3 + x = 105 Comment

Guess Comment 468 Too small 5130 Too big Too small Try the value half- way between 4 and 5 Too small Too big To decide if the solution is closer to 4.6 or 4.7, try the middle value 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 decimal place We only need the answer correct to one decimal place X = 4.65 was too big. X = 4.65 was too big. So your next guess would be smaller So your next guess would be smaller You could try 4.64 or 4.63 You could try 4.64 or 4.63 All these would be 4.6 correct to 1 decimal place All these would be 4.6 correct to 1 decimal place So correct to one decimal place x would equal 4.6

Using trial and improvement show that the equation 3X 2 - 4x = 18 has a solution between 3 and 4 Set up your table of values

Guess 3X 2 - 4x = 18 Comment

Guess Comment 315 Too small 432 Too big Too big Try the value half- way between 3 and 4 Too big Too big To decide if the solution is closer to 3.2 or 3.3, try the middle value 3.25 The solution is between 3.2 and 3.3 remember, we cannot just guess which is closer Too small Too big Remember to write down all the digits on your calculator

We only need the answer correct to one decimal place We only need the answer correct to one decimal place X = 3.25 was too big. X = 3.25 was too big. So your next guess would be smaller So your next guess would be smaller So you could try 3.24 or 3.23 So you could try 3.24 or 3.23 All these would be 3.2 correct to 1 decimal place All these would be 3.2 correct to 1 decimal place So correct to one decimal place x would equal 3.2