solve the equation then check your solution  1.4 f + 1.1 = 8.3 - f

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embizze eNotes educator| Certified Educator

Solve the equation 1.4f=1.1=8.3-f

This is a linear equation in one variable. There are a number of ways to find the solution to such an equation. For instance we could use a guess and refine approach; but this is very inefficient.

We could graph the left and right sides of the equation separately and look for the intersection. This works well if the solution lies on a lattice point (a point with integral or rational coordinates). Here we would graph y=1.4f+1.1 and y=8.3-f thus:

The intersection occurs (assuming we are graphing f versus y) at f=3.

A much more common and efficient way is to transform the equation into equivalent equations using properties of equality.

1.4f+1.1=8.3-f           Given

2.4f+1.1=8.3             Add f to both sides. This gets the variable on one side.

2.4f=7.2                    Subtract 1.1 from both sides. This isolates the term with

                                the variable.

f=3                           Divide both sides by 2.4

Check: 1.4(3)+1.1=4.2+1.1=5.3

and 8.3-3=5.3 so the solution works.

An efficient algorithm for any linear equation in one variable is:

(1) Eliminate any parantheses, using the distributive property.

(2) Get the variable on one side of the equation.

(3) Add/subtract any number being added to or subtracted from the term that contains the variable to both sides.

(4) Divide both sides by the coefficient on the variable.


The solution is f=3