SBP-Program

f

tw

in

Solving linear equations with fractions

Example.

Solve the equation

2x = 3
54

Solution.

To solve the equation, we have to find the value of the variable x.

We want to get the x by itself. We isolate the variable x by dividing both sides of the equation by 2/5

2x ÷ 2 = 3 ÷ 2
5545
x * 2 ÷ 2 = 3 ÷ 2
15545

It is obvious that

2 ÷ 2 = 1
55

Hence

x * 1 = 3 ÷ 2
145
x = 3 ÷ 2
45

How to divide fractions? See Rules for dividing fractions.

We take the right-hand side of the equation

3 ÷ 2
45

1. Invert the second fraction (the divisor) to get its reciprocal.

The reciprocal for 2/5 is 5/2.

2. Multiply the first fraction (the dividend) by the reciprocal

3 * 5 = 15
428

So, we have the solution of the linear equation

x = 15
8

We should check the solution by substitution 15/8 into the original linear equation

2x = 3
54
2 * 15 = 3
584
30 = 3
404
3 *  10  = 3
4 *  10 4
3 = 3
44

The left side equals the right side.

This means that the solution

x = 15 = 17
88

is correct.