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.

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The solution is f=3

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