LEMMA

Equations & inequalities

Variables on both sides

ALEKS placementTEAS math

Collect variables on one side and constants on the other, then finish like a two-step.

What this covers

  • Picture two piles that must stay equal. Take the same number of x's off both piles, and the same plain numbers.
  • Distribute and combine like terms on each side first.
  • Add or subtract a variable term to clear it from one side. Removing the smaller x-term keeps the count positive.
  • Either side works: remove 2x from both or 5x from both. Both are allowed; one is tidier.
  • Move the constants to the opposite side, then divide by the remaining coefficient.
  • x can end up on the right. 5 = 3x says the same thing as 3x = 5.
  • Check by putting your answer into both sides. Each side should come to the same number.

Worked example

Worked example

Solve 5x - 3 = 2x + 12.

  1. 3x−3=12Subtract 2x from both sides.
  2. 3x=15Add 3 to both sides.
  3. x=5Divide by 3.
Another worked example

Solve 6(x − 2) = 3x − 21.

  1. 6x−12=3x−21Distribute 6 to both terms inside the parentheses first.
  2. 3x−12=−21Subtract 3x from both sides so x appears on one side only.
  3. 3x=−9Add 12 to both sides.
  4. x=−3Divide both sides by 3. Check: 6(−5) = −30 and 3(−3) − 21 = −30.

A common mistake

A mistake Lemma catches

From 3x−3=12

3x=93x=15

“To clear -3 from the left side, add 3 to both sides: 12 + 3 = 15. Instead 3 was subtracted from the right side: 12 - 3 = 9, so the two sides no longer balance.”

Try one

Sample problem

Solve for x.

3x−6=x+12

Practice both sides 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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