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 12835 September 3, 2019
Two-step inequalities – Integers – easy 463.3 kB 12611 September 3, 2019
Two-step inequalities – Integers – medium 463.2 kB 18920 September 3, 2019
Two-step inequalities – Integers – hard 464.4 kB 7554 September 3, 2019
Two-step inequalities – Integers – very hard 463.3 kB 5398 September 3, 2019
Decimals
Two-step inequalities – Decimals – very easy 463.7 kB 3134 September 3, 2019
Two-step inequalities – Decimals – easy 463.6 kB 2651 September 3, 2019
Two-step inequalities – Decimals – medium 463.6 kB 2882 September 3, 2019
Two-step inequalities – Decimals – hard 463.4 kB 1877 September 3, 2019
Two-step inequalities – Decimals – very hard 463.4 kB 1660 September 3, 2019
Fractions
Two-step inequalities – Fractions – very easy 467 kB 4427 September 3, 2019
Two-step inequalities – Fractions – easy 466.9 kB 3506 September 3, 2019
Two-step inequalities – Fractions – medium 467.4 kB 3821 September 3, 2019
Two-step inequalities – Fractions – hard 467.4 kB 2314 September 3, 2019
Two-step inequalities – Fractions – very hard 467.6 kB 2494 September 3, 2019

Two-step inequalities worksheets for students

Worksheet Name File Size Downloads Upload date
Two-step inequalities – Integers 4.4 MB 9259 September 3, 2019
Two-step inequalities – Decimals 5.3 MB 2832 September 3, 2019
Two-step inequalities – Fractions 5.6 MB 3064 September 3, 2019