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 10106 January 1, 1970
Two-step inequalities – Integers – easy 0 B 9978 January 1, 1970
Two-step inequalities – Integers – medium 0 B 14887 January 1, 1970
Two-step inequalities – Integers – hard 0 B 5826 January 1, 1970
Two-step inequalities – Integers – very hard 0 B 4139 January 1, 1970
Decimals
Two-step inequalities – Decimals – very easy 0 B 2345 January 1, 1970
Two-step inequalities – Decimals – easy 0 B 1946 January 1, 1970
Two-step inequalities – Decimals – medium 0 B 2036 January 1, 1970
Two-step inequalities – Decimals – hard 0 B 1309 January 1, 1970
Two-step inequalities – Decimals – very hard 0 B 1144 January 1, 1970
Fractions
Two-step inequalities – Fractions – very easy 0 B 3494 January 1, 1970
Two-step inequalities – Fractions – easy 0 B 2701 January 1, 1970
Two-step inequalities – Fractions – medium 0 B 2955 January 1, 1970
Two-step inequalities – Fractions – hard 0 B 1750 January 1, 1970
Two-step inequalities – Fractions – very hard 0 B 1790 January 1, 1970


Two-step inequalities worksheets for students

Worksheet Name File Size Downloads Upload date
Two-step inequalities – Integers 0 B 7121 January 1, 1970
Two-step inequalities – Decimals 0 B 2108 January 1, 1970
Two-step inequalities – Fractions 0 B 2382 January 1, 1970


Two-step inequalities knowledge test