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 10326 January 1, 1970
Two-step inequalities – Integers – easy 0 B 10199 January 1, 1970
Two-step inequalities – Integers – medium 0 B 15151 January 1, 1970
Two-step inequalities – Integers – hard 0 B 5962 January 1, 1970
Two-step inequalities – Integers – very hard 0 B 4220 January 1, 1970
Decimals
Two-step inequalities – Decimals – very easy 0 B 2395 January 1, 1970
Two-step inequalities – Decimals – easy 0 B 1994 January 1, 1970
Two-step inequalities – Decimals – medium 0 B 2069 January 1, 1970
Two-step inequalities – Decimals – hard 0 B 1337 January 1, 1970
Two-step inequalities – Decimals – very hard 0 B 1166 January 1, 1970
Fractions
Two-step inequalities – Fractions – very easy 0 B 3561 January 1, 1970
Two-step inequalities – Fractions – easy 0 B 2752 January 1, 1970
Two-step inequalities – Fractions – medium 0 B 3014 January 1, 1970
Two-step inequalities – Fractions – hard 0 B 1794 January 1, 1970
Two-step inequalities – Fractions – very hard 0 B 1837 January 1, 1970


Two-step inequalities worksheets for students

Worksheet Name File Size Downloads Upload date
Two-step inequalities – Integers 0 B 7230 January 1, 1970
Two-step inequalities – Decimals 0 B 2147 January 1, 1970
Two-step inequalities – Fractions 0 B 2422 January 1, 1970


Two-step inequalities knowledge test