SBP-Program

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Solving linear equations with fractions and whole numbers

Look at the example of solving linear equations with fractions and whole numbers. There is nothing hard to understand here.

Example.

Solve the equation

30 + 2x = 2x + 2
3

Solution.

We are finding out a value of the unknown x that makes the equality true.

We collect all the terms containing the unknown x on the left-hand side and whole numbers on the right-hand side of the equation.

We transpose 2x/3 from the right side to the left side by changing its sign

30 + 2x - 2x = 2
3

Then we transpose 30 from the left side to the right side by changing its sign

2x - 2x = 2 - 30
3

Now all the terms containing x are on the left and all the whole numbers are on the right.

Simplify the equation

2x * 3 - 2x = -28
33
6x - 2x = -28
3
4x = -28
3

Multiply either side by 3

4x * 3 = -28 * 3
3
4x = -84

Divide both sides by 4 to obtain the unknown x on its own

4x ÷ 4 = -84 ÷ 4
x = -21

So, the solution of the linear equation is x = -21.

Is this solution correct?

To check the solution, we put the value (-21) of the unknown x in the equation

30 + 2x = 2x + 2
3
30 + 2 * (-21) = 2 * (-21) + 2
3
30 - 42 = -42 + 2
3
-12 = -36
3
-12 = -12

The both sides of the equation are equal. It means that our solution x = -21 is correct.