# Two-step inequalities

Two-step inequalities are to one-step inequalities what two-step equations are to one-step equations – the same thing, but a bit more work is needed in order to solve them. Two-step inequalities are very easy to solve and the rules you have to adhere to are the same as for the one-step inequalities – remember that you need to change the sign of inequality when multiplying or dividing the whole inequality with a negative number. The order of operations will not come into play often since there are not many operations to perform here.

We will now show you on this example how this inequality looks like and what it takes to solve it:

4x + 8 > 20

The first thing you need to do is to put all the numbers on the right side and the variables on the left. Then perform the additions and subtractions. Like this:

4x > 20 – 8

4x > 12

The only thing left to do now is to divide the whole inequality by 4 to get the final, simplified result. Since the number we are dividing the inequality by is positive, it is not necessary to change the sign of inequality. Therefore:

4x > 12 |:4

x > 3

And now we have the final result. If you wish to practice solving two-step inequalities a bit more, please feel free to use the worksheets below.

## Two-step inequalities exams for teachers

 Exam Name File Size Downloads Upload date Integers Two-step inequalities – Integers – very easy 463.2 kB 9182 October 13, 2012 Two-step inequalities – Integers – easy 463.3 kB 9119 October 13, 2012 Two-step inequalities – Integers – medium 463.2 kB 13704 October 13, 2012 Two-step inequalities – Integers – hard 464.4 kB 5350 October 13, 2012 Two-step inequalities – Integers – very hard 463.3 kB 3826 October 13, 2012 Decimals Two-step inequalities – Decimals – very easy 463.7 kB 2110 October 13, 2012 Two-step inequalities – Decimals – easy 463.6 kB 1754 October 13, 2012 Two-step inequalities – Decimals – medium 463.6 kB 1852 October 13, 2012 Two-step inequalities – Decimals – hard 463.4 kB 1202 October 13, 2012 Two-step inequalities – Decimals – very hard 463.4 kB 1063 October 13, 2012 Fractions Two-step inequalities – Fractions – very easy 467 kB 3143 October 13, 2012 Two-step inequalities – Fractions – easy 466.9 kB 2477 October 13, 2012 Two-step inequalities – Fractions – medium 467.4 kB 2700 October 13, 2012 Two-step inequalities – Fractions – hard 467.4 kB 1616 October 13, 2012 Two-step inequalities – Fractions – very hard 467.6 kB 1625 October 13, 2012

## Two-step inequalities worksheets for students

 Worksheet Name File Size Downloads Upload date Two-step inequalities – Integers 4.4 MB 6518 October 14, 2012 Two-step inequalities – Decimals 5.3 MB 1924 October 14, 2012 Two-step inequalities – Fractions 5.6 MB 2200 October 14, 2012