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

two step inequalities

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 9772 October 13, 2012
Two-step inequalities – Integers – easy 463.3 kB 9710 October 13, 2012
Two-step inequalities – Integers – medium 463.2 kB 14469 October 13, 2012
Two-step inequalities – Integers – hard 464.4 kB 5633 October 13, 2012
Two-step inequalities – Integers – very hard 463.3 kB 4013 October 13, 2012
Decimals
Two-step inequalities – Decimals – very easy 463.7 kB 2291 October 13, 2012
Two-step inequalities – Decimals – easy 463.6 kB 1916 October 13, 2012
Two-step inequalities – Decimals – medium 463.6 kB 1974 October 13, 2012
Two-step inequalities – Decimals – hard 463.4 kB 1310 October 13, 2012
Two-step inequalities – Decimals – very hard 463.4 kB 1144 October 13, 2012
Fractions
Two-step inequalities – Fractions – very easy 467 kB 3339 October 13, 2012
Two-step inequalities – Fractions – easy 466.9 kB 2649 October 13, 2012
Two-step inequalities – Fractions – medium 467.4 kB 2875 October 13, 2012
Two-step inequalities – Fractions – hard 467.4 kB 1710 October 13, 2012
Two-step inequalities – Fractions – very hard 467.6 kB 1732 October 13, 2012

Two-step inequalities worksheets for students

Worksheet Name File Size Downloads Upload date
Two-step inequalities – Integers 4.4 MB 6919 October 14, 2012
Two-step inequalities – Decimals 5.3 MB 2059 October 14, 2012
Two-step inequalities – Fractions 5.6 MB 2348 October 14, 2012

Two-step inequalities knowledge test