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 9788 January 1, 1970
Two-step inequalities – Integers – easy 0 B 9689 January 1, 1970
Two-step inequalities – Integers – medium 0 B 14530 January 1, 1970
Two-step inequalities – Integers – hard 0 B 5678 January 1, 1970
Two-step inequalities – Integers – very hard 0 B 4058 January 1, 1970
Decimals
Two-step inequalities – Decimals – very easy 0 B 2276 January 1, 1970
Two-step inequalities – Decimals – easy 0 B 1888 January 1, 1970
Two-step inequalities – Decimals – medium 0 B 1987 January 1, 1970
Two-step inequalities – Decimals – hard 0 B 1279 January 1, 1970
Two-step inequalities – Decimals – very hard 0 B 1119 January 1, 1970
Fractions
Two-step inequalities – Fractions – very easy 0 B 3402 January 1, 1970
Two-step inequalities – Fractions – easy 0 B 2640 January 1, 1970
Two-step inequalities – Fractions – medium 0 B 2893 January 1, 1970
Two-step inequalities – Fractions – hard 0 B 1708 January 1, 1970
Two-step inequalities – Fractions – very hard 0 B 1746 January 1, 1970


Two-step inequalities worksheets for students

Worksheet Name File Size Downloads Upload date
Two-step inequalities – Integers 0 B 6938 January 1, 1970
Two-step inequalities – Decimals 0 B 2056 January 1, 1970
Two-step inequalities – Fractions 0 B 2312 January 1, 1970


Two-step inequalities knowledge test