Worksheets · Algebra 1

Equations with variables on both sides worksheet

The first move is to get every variable term onto one side and every number onto the other. Which side you choose does not matter, but choosing the one that leaves a positive coefficient saves a sign error later.

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Pick more than one for a sheet that mixes them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Variables on Both Sides

Date Period

Solve each equation, or answer as asked.

  1. Distribute, then solve

    9+4(m−9)=7m−6
  2. 2(k+6)=14+k
  3. −2(1−m)=m+4
  4. −3n+7=−(5−n)
  5. 2n=−2(n−1)−10
  6. −17−5n=−4(n+3)
  7. 7p+20=−4(1−p)

  1. Solve with fraction or decimal coefficients

    0.2x+4=x+12
  2. a4+1=a−5
  3. x2−3=x4−2
  4. 43n+4=n+8
  5. 1.25k−7=0.75k−2
  6. 1.5k+9=−3k−9
  7. m2+10=m6+8

  1. Distribute and combine like terms, then solve

    2(y+1)+3y=3y−20
  2. −11+4(a−3)+8=a
  3. 2m=2(m−7)−m+5
  4. 8x+13=−5(x+1)−5x
  5. 6m+12−(m+9)=8m
  6. 6(r+8)=−5r−6r−3

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Variables on Both SidesAnswer keyVersion 1

Date Period

Solve each equation, or answer as asked.

  1. Distribute, then solve

    9+4(m−9)=7m−6{−7}
  2. 2(k+6)=14+k{2}
  3. −2(1−m)=m+4{6}
  4. −3n+7=−(5−n){3}
  5. 2n=−2(n−1)−10{−2}
  6. −17−5n=−4(n+3){−5}
  7. 7p+20=−4(1−p){−8}

  1. Solve with fraction or decimal coefficients

    0.2x+4=x+12{−10}
  2. a4+1=a−5{8}
  3. x2−3=x4−2{4}
  4. 43n+4=n+8{12}
  5. 1.25k−7=0.75k−2{10}
  6. 1.5k+9=−3k−9{−4}
  7. m2+10=m6+8{−6}

  1. Distribute and combine like terms, then solve

    2(y+1)+3y=3y−20{−11}
  2. −11+4(a−3)+8=a{5}
  3. 2m=2(m−7)−m+5{−9}
  4. 8x+13=−5(x+1)−5x{−1}
  5. 6m+12−(m+9)=8m{1}
  6. 6(r+8)=−5r−6r−3{−3}

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

5x−14=8x+4

  1. Take 5x from both sides: -14 = 3x + 4.
  2. Take 4 from both sides: -18 = 3x.
  3. Divide by 3.

The answer is {−6}.

Where students go wrong

Moving a term across without changing its sign. Subtracting 5x from both sides is what makes it vanish on the left, and the same subtraction is what makes 8x into 3x on the right.

Also called variable on both sides or solving equations both sides.

What you can put on this worksheet

Both sides: plain, then parentheses
8+8a=4+9a → {4}
Like terms, then fractions and decimals
7+7y−1=5y+4 → {−1}
Sentences, combining, or no solution and identities
Fifteen less than four times a number is the same as the number. Let n be the number. → 4n−15=n; n=5

Questions about these worksheets

Yes. Every equations with variables on both sides sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the equations with variables on both sides questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: both sides: plain, then parentheses, like terms, then fractions and decimals and sentences, combining, or no solution and identities. Tick as many as you want and set how many of each, or let it spread them evenly.

Moving a term across without changing its sign. Subtracting 5x from both sides is what makes it vanish on the left, and the same subtraction is what makes 8x into 3x on the right.