Math Buddyv1.0

Solve for a variable calculator

Type a formula and the letter you want. MathBuddy rearranges it step by step.

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What this page covers

  • Rearranging formulas from geometry and everyday algebra, such as area, perimeter and temperature.
  • Formulas where the letter sits inside a fraction or is multiplied by other letters.
  • Formulas where the letter appears twice, by collecting it on one side and factoring it out.
  • Not covered here: equations with a single letter and numbers only (use Solve linear equations with steps) and finding numbers for several unknowns at once.

How to enter the problem

  • Start with Solve for and the letter, then the formula, such as Solve for h: A = 1/2 bh.
  • 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 P=2l+2w\displaystyle P = 2l + 2w for w\displaystyle w.

Answer

Verified

The answer is

w=P−2l2w = \frac{P - 2l}{2}

Explanation

  1. Move the term without w
    Subtract 2l2l from both sides
    P−2l=2wP - 2l = 2w
  2. Undo the multiplication
    Divide both sides by 22
    w=P−2l2w = \frac{P - 2l}{2}

Example 2

Problem

Solve F=95C+32\displaystyle F = \frac{9}{5}C + 32 for C\displaystyle C.

Answer

Verified

The answer is

C=5(F−32)9C = \frac{5(F - 32)}{9}

Explanation

  1. Undo the addition first
    Subtract 3232
    F−32=95CF - 32 = \frac{9}{5}C
  2. Undo the multiplication
    Multiply both sides by 59\frac{5}{9}
    C=59(F−32)C = \frac{5}{9}(F - 32)
  3. Write it as one fraction

Example 3

Problem

Solve ax+b=cx+d\displaystyle ax + b = cx + d for x\displaystyle x.

Answer

Verified

The answer is

x=d−ba−cx = \frac{d - b}{a - c}

Explanation

  1. Collect the x terms on one side
    Subtract cxcx and bb from both sides
    ax−cx=d−bax - cx = d - b
  2. Factor out x
    x(a−c)=d−bx(a - c) = d - b
  3. Divide
    x=d−ba−cx = \frac{d - b}{a - c}, which needs a≠ca \neq c.

Common mistakes

  • Dividing only one term. From P−2l=2wP - 2l = 2w, the whole left side is divided by 2, so w=P−lw = P - l is wrong.
  • Undoing operations in the wrong order. In F=95C+32F = \frac{9}{5}C + 32, remove the +32+32 before dealing with the 95\frac{9}{5}.
  • Leaving the chosen letter on both sides. Collect every term that contains it on one side, then factor it out.
  • Dividing by an expression that could be zero without saying so, such as a−ca - c when a=ca = c.

Checks, assumptions and limits

  • Substitute numbers. With b=6b = 6 and h=4h = 4, A=12⋅6⋅4=12A = \frac{1}{2} \cdot 6 \cdot 4 = 12, and 2⋅126=4\frac{2 \cdot 12}{6} = 4 gives back hh.
  • Dividing by a letter assumes it is not zero: h=2Abh = \frac{2A}{b} needs b≠0b \neq 0.
  • Units carry through. If A is in square metres and b in metres, h comes out in metres.
  • MathBuddy can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

It means rewriting the formula so the letter you want stands alone on one side and everything else is on the other. The other letters stay as letters.

Start with the words Solve for and the letter, then the formula, for example: Solve for h: A = 1/2 bh.

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

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Last updated: · MathBuddy