Inequalities Calculator

Use <, <=, >, >= or !=. Absolute values as |2x - 3| or abs(2x - 3). Compound form such as -3 <= 2x + 1 < 7 is accepted.
Solution in interval notation
(-∞, -12)
Inequality Calculator
Solution in inequality notation
x < -12
Solution in set-builder notation
{x ∈ ℝ : x < -12}
Shape of the solution set
single interval
Number of intervals
1
Every real number is a solution
no
No solution
no
Inequality as read
3x + 5 < 2x - 7
Degree of the collected expression
1
Worked out from OpenStax, Elementary Algebra 2e, section 2.7: Solve Linear Inequalities, and section 2.7 compound inequalities and 1 other source.

How this is worked out

5 steps
  1. Read as: 3x + 5 < 2x - 7.
  2. Collect everything on one side: f(x) < 0.
  3. Critical numbers: -12.
  4. Test one point in each interval between the critical numbers, and test the critical numbers themselves.
  5. Solution: (-∞, -12)
Endpoints of the solution settable
-12
Critical numbers testedtable
-12
Sign charttable
intervaltestPointvaluesignsatisfied
(-∞, -12)-24-12-yes
(-12, ∞)012+no

Results are general information, not financial, tax, legal, medical or engineering advice.