How this calculator works
Subtract b from both sides, then divide by a. Dividing by a negative value reverses the comparison. A strict inequality has an open endpoint and an inclusive comparison has a closed endpoint. The interval and text instructions describe the same number-line region. A constant inequality shades everything or nothing.
Formula
ax + b < c gives x < (c-b)/a when a > 0 and x > (c-b)/a when a < 0. The same reversal applies to inclusive comparisons.
Worked example
For -2x + 3 <= 7, subtract 3 to get -2x <= 4. Divide by -2 and reverse the comparison: x >= -2. Use a closed point at -2 and shade right, or write [-2, inf).
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Frequently asked questions
Where is the plotted number line?
The current tool provides exact interval notation and endpoint and shading instructions as text.
Can a be zero?
Yes. The comparison then has a constant truth value and no finite endpoint.
What does inf mean?
It means infinity. Infinity is never included as an endpoint, so its side always uses a parenthesis.