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 0 B 9469 January 1, 1970
Two-step inequalities – Integers – easy 0 B 9396 January 1, 1970
Two-step inequalities – Integers – medium 0 B 14103 January 1, 1970
Two-step inequalities – Integers – hard 0 B 5507 January 1, 1970
Two-step inequalities – Integers – very hard 0 B 3957 January 1, 1970
Decimals
Two-step inequalities – Decimals – very easy 0 B 2214 January 1, 1970
Two-step inequalities – Decimals – easy 0 B 1824 January 1, 1970
Two-step inequalities – Decimals – medium 0 B 1920 January 1, 1970
Two-step inequalities – Decimals – hard 0 B 1251 January 1, 1970
Two-step inequalities – Decimals – very hard 0 B 1093 January 1, 1970
Fractions
Two-step inequalities – Fractions – very easy 0 B 3286 January 1, 1970
Two-step inequalities – Fractions – easy 0 B 2549 January 1, 1970
Two-step inequalities – Fractions – medium 0 B 2788 January 1, 1970
Two-step inequalities – Fractions – hard 0 B 1667 January 1, 1970
Two-step inequalities – Fractions – very hard 0 B 1693 January 1, 1970


Two-step inequalities worksheets for students

Worksheet Name File Size Downloads Upload date
Two-step inequalities – Integers 0 B 6743 January 1, 1970
Two-step inequalities – Decimals 0 B 1998 January 1, 1970
Two-step inequalities – Fractions 0 B 2257 January 1, 1970


Two-step inequalities knowledge test