IXL - Approximate solutions using a table (Algebra 1 practice)

Use the table to estimate one solution, to the nearest tenth, of this equation:

The values in the table have been rounded to the nearest tenth.

x	4 x + 3	3 x
1	7	3
2	11	9
3	15	27
2.2	11.8	11.2
2.3	12.2	12.5
2.25	12	11.8

≈

ref_doc_title.

Learn with an example

question

Use the table to estimate one solution, to the nearest tenth, of this equation:

–

The values in the table have been rounded to the nearest tenth.

x	– 2 x + 6	3 x
0	6	1
1	4	3
2	2	9
1.1	3.8	3.3
1.2	3.6	3.7
1.15	3.7	3.5

≈

key idea

Any value of

that makes

(

)

and

(

)

equal is a solution of the equation

(

)

(

)

One way to find a solution of

(

)

(

)

is to try several

-values

that make the difference between

(

)

and

(

)

smaller and smaller. This method is called using successive

approximations.

solution

Look at the equation

–

You can think of the left side as the function

(

)

–

Similarly, you can think of the right side as the function

(

)

Now look at the table. The second and third columns give you values for the functions

(

)

and

(

)

Notice that when

1.1

(

)

is greater than

(

)

but when

1.2

(

)

is less than

(

)

x	f ( x ) = – 2 x + 6	g ( x ) = 3 x
0	6	1
1	4	3
2	2	9
1.1	3.8	3.3
1.2	3.6	3.7
1.15	3.7	3.5

This means that there is an

-value

between

1.1

and

1.2

that makes

(

)

equal to

(

)

In the last row, when

1.15

(

)

is greater than

(

)

Since

(

)

is greater than

(

)

when

1.15

but less than

(

)

when

1.2

the solution of

–

is between

1.15

and

1.2

Values between 1.15 and 1.2 round up to 1.2. So,

≈

1.2

is one solution, to the nearest tenth, of

–

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