Math Buddyv1.0

Inequality calculator with steps

Type or scan an inequality. MathBuddy solves it step by step and gives the solution interval.

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What this page covers

  • Linear inequalities, including fractions and dividing by a negative number.
  • Absolute value inequalities, turned into a double inequality.
  • Quadratic inequalities, solved with the roots and a sign check.
  • Not covered here: drawing the graph of the solution, and inequalities in two variables. For the matching equation, use Solve an equation for x.

How to enter the problem

  • Type it with <, >, <= or >=, or use the inequality keys on the math keyboard.
  • Scan it. Fit the one problem in the frame.
  • Choose a photo. Several problems in one photo are solved as a list.
  • Then tap Solve.

Worked examples

Example 1

Problem

Solve x2−1>x+34\displaystyle \frac{x}{2} - 1 > \frac{x + 3}{4}.

Answer

Verified

The answer is

x>7x > 7

Explanation

  1. Clear the fractions
    Multiply every term by 44, a positive number, so the sign stays: 2x−4>x+32x - 4 > x + 3.
  2. Collect the x terms
    Subtract xx: x−4>3x - 4 > 3.
  3. Isolate x
    Add 44: x>7x > 7.

Example 2

Problem

Solve ∣x−2∣≤5\displaystyle |x - 2| \leq 5.

Answer

Verified

The answer is

[−3,7][-3, 7]

Explanation

  1. Write it as a double inequality
    A distance of at most 55 from 22 means −5≤x−2≤5-5 \leq x - 2 \leq 5.
  2. Add 2 to every part
    −3≤x≤7-3 \leq x \leq 7.
  3. Write it as an interval
    Both ends are included, so use square brackets.

Example 3

Problem

Solve x2−x−6<0\displaystyle x^2 - x - 6 < 0.

Answer

Verified

The answer is

(−2,3)(-2, 3)

Explanation

  1. Find where the left side is zero
    x2−x−6=(x−3)(x+2)x^2 - x - 6 = (x - 3)(x + 2), which is zero at x=−2x = -2 and x=3x = 3.
  2. Test one point in each region
    x=−3x = -3: (−6)(−1)=6>0(-6)(-1) = 6 > 0. x=0x = 0: (−3)(2)=−6<0(-3)(2) = -6 < 0. x=4x = 4
    (1)(6)=6>0(1)(6) = 6 > 0
  3. Keep the negative region
    The product is negative only between the roots, and the roots themselves give 00, which is not less than 00.

Common mistakes

  • Forgetting to flip the sign when dividing by a negative. −2x≥6-2x \geq 6 gives x≤−3x \leq -3, not x≥−3x \geq -3.
  • Answering a quadratic inequality with its roots only. x2−x−6<0x^2 - x - 6 < 0 is solved by an interval, not by x=−2x = -2 and x=3x = 3.
  • Keeping only one side of an absolute value inequality. ∣x−2∣≤5|x - 2| \leq 5 also needs x−2≥−5x - 2 \geq -5.
  • Using a square bracket at infinity. Write (7,∞)(7, \infty), never (7,∞](7, \infty].

Checks, assumptions and limits

  • Test a point. In −2x+7≥13-2x + 7 \geq 13, x=−4x = -4 gives 15≥1315 \geq 13, true, and x=0x = 0 gives 7≥137 \geq 13, false.
  • A round bracket means the endpoint is left out (< or >); a square bracket means it is included (<= or >=).
  • Multiplying or dividing both sides by a negative number reverses the inequality sign; adding or subtracting never does.
  • MathBuddy can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

Shade the interval. Use an open circle at an endpoint with a round bracket and a filled circle at one with a square bracket. For (-2, 3), shade between -2 and 3 with both circles open.

Multiplying or dividing by a negative number reverses order. 2 is less than 5, but -2 is greater than -5. So the inequality sign must turn around for the statement to stay true.

Yes. Use the camera on the one inequality, or choose a photo. Several problems in one photo are solved as a list.

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