LEMMA

Equations & inequalities

Literal equations

ALEKS placementTEAS math

Solve for a letter exactly as you would for x — every other letter acts like a fixed number.

What this covers

  • Decide which letter is the target. Every other letter is a number you happen not to know yet.
  • Ask what is attached to the target, then undo it, outermost first: added terms come off before anything multiplying.
  • Stuck? Write a number twin beside it: A = ½bh next to 8 = ½·4x. Make the same move on both lines.
  • Whatever multiplies the target, divide by all of it only when it is nonzero. A fraction in front comes off by multiplying by its flip.
  • Factor the target out if it appears in more than one term, then divide by the whole bracket.
  • Finish with the target letter written first: b = 2A/h reads as an answer; 2A/h = b hides it.

Worked example

Worked example

Solve A = ½bh for b, assuming h ≠ 0.

  1. 2A=bhMultiply both sides by 2 to clear the half, the same move as on 8 = ½·4x.
  2. b=h2A​Since h ≠ 0, divide both sides by h and write b first.
Another worked example

Solve y = mx + b for x.

  1. y−b=mxSubtract b from both sides.
  2. x=my−b​,m=0Divide only if the parameter m is nonzero.
  3. m=0:y=bIf m = 0, all x work when y = b; otherwise none work.

A common mistake

A mistake Lemma catches

From y=mx+b

y+b=mxy−b=mx

“To clear b from the right side, subtract b from both sides: y − b = mx + b − b = mx. Adding b on the left instead gives y + b, and the two sides no longer balance.”

Try one

Sample problem

Solve the perimeter formula for l.

P=2l+2w

Practice literal equations free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

Where this fits

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