LEMMA

Equations & inequalities

Two-step equations

ALEKS placementTEAS math

Undo addition first, then multiplication — the reverse of the order of operations.

What this covers

  • Building 3x + 4 multiplied first, then added. Undoing runs backwards: take off the 4, then undo the 3.
  • Move the constant away from the variable term by adding or subtracting the same amount on both sides.
  • The coefficient is the number stuck to x by multiplication. Division undoes it, so divide both sides by it.
  • A fraction in front of x comes off by multiplying both sides by its flip.
  • Check by putting the answer back: 3 times 5 plus 4 should give 19.

Worked example

Worked example

Solve 3x + 4 = 19.

  1. 3x=15Subtract 4 from both sides.
  2. x=5Divide both sides by 3.
Another worked example

Solve 5 − 6x = 35.

  1. −6x=30Subtract 5 from both sides. The x term keeps its negative sign: it is −6x, not 6x.
  2. x=−5Divide both sides by −6. Check: 5 − 6(−5) = 5 + 30 = 35.

A common mistake

A mistake Lemma catches

From 3x+4=19

3x=233x=15

“To clear 4 from the left side, subtract 4 from both sides: 19 - 4 = 15. Instead 4 was added to the right side: 19 + 4 = 23, so the two sides no longer balance.”

Try one

Sample problem

Solve for x. Show one useful line at a time.

−4x+9=−19

Practice two-step 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

Before this

After this