somokai.

Equations with x on both sides

First we collect all the x terms on one side by subtracting the smaller x term from both sides. Then we collect the numbers on the other side and divide by the number in front of x. Finally we check the answer.

Years 7–9 · Updated

Watch Fox work it out on the board

Fox works one step at a time. Press play.

Solve your own task

Write the task. You get one step at a time.

The goal: every x on one side

We want to collect all the x terms on one side and then get x on its own.

6x + 5 = 2x + 21

We take the same x term away from both sides. The sides are then still equal, like balance scales where we lift the same amount off each pan.

  • Collect x on one side: subtract (or add) the same x term on both sides.
  • Collect the numbers on the other side in the same way.
  • Divide both sides by the number in front of x.
  • Check: put in the answer and work out each side separately.

When the x term has a minus sign

If it says −3x, we add 3x to both sides, because −3x + 3x = 0.

4 − 3x + 3x = x − 8 + 3x

Example

Example 1: 6x + 5 = 2x + 21

We want to collect all the x terms on one side. We take away the smaller x term, 2x.

  1. We subtract 2x from both sides. Then the sides are still equal.

    6x + 5 − 2x = 2x + 21 − 2x

  2. 6x − 2x = 4x. On the right, 2x − 2x = 0.

    4x + 5 = 21

  3. We subtract 5 from both sides.

    4x + 5 − 5 = 21 − 5

  4. What is left is four x, which together make 16.

    4x = 16

  5. We divide both sides by 4.

    4x ÷ 4 = 16 ÷ 4

  6. Now we have x on its own.

    x = 4

Left: 6 · 4 + 5 = 29. Right: 2 · 4 + 21 = 29. The sides are equal, so x = 4 is correct.

Example 2: 4 − 3x = x − 8

We want to collect all the x terms on one side. We get rid of −3x by adding 3x.

  1. We add 3x to both sides, because −3x + 3x = 0.

    4 − 3x + 3x = x − 8 + 3x

  2. On the right, x + 3x = 4x.

    4 = 4x − 8

  3. We add 8 to both sides.

    4 + 8 = 4x − 8 + 8

  4. That leaves 12 on the left and 4x on the right.

    12 = 4x

  5. We divide both sides by 4. 3 = x means the same as x = 3.

    x = 3

Left: 4 − 3 · 3 = −5. Right: 3 − 8 = −5. The sides are equal, so x = 3 is correct.

Example 3: when do two gyms cost the same?

Gym A: 300 kr plus 150 kr/month. Gym B: 250 kr/month. After how many months, x, do they cost the same?

  1. After x months A costs 300 + 150x kr and B costs 250x kr. Setting the costs equal gives an equation.

    300 + 150x = 250x

  2. We subtract 150x from both sides.

    300 + 150x − 150x = 250x − 150x

  3. On the right, 250x − 150x = 100x.

    300 = 100x

  4. We divide both sides by 100.

    x = 3

A: 300 + 150 · 3 = 750 kr. B: 250 · 3 = 750 kr. After 3 months you have paid the same amount.

Pitfalls

  • Adding the x term instead, so that 6x + 5 = 2x + 21 becomes 8x + 5 = 21.

    2x − 2x = 0, so we subtract 2x from both sides: 4x + 5 = 21.

  • Changing only one side, so that 6x + 5 = 2x + 21 becomes 6x + 5 = 21.

    Write out the step with both sides: 6x + 5 − 2x = 2x + 21 − 2x.

  • Answering x = 12 when it says 12 = 4x.

    12 = 4x is the same as 4x = 12. Divide both sides by 4: x = 3.

Practise on your own

0 of 4 correct

  1. Solve the equation 5x + 2 = 3x + 10.

  2. Solve the equation 9x − 7 = 5x + 13.

  3. Solve the equation 14 − 2x = 3x − 6.

  4. Solve the equation 3x + 11 = 7x + 2. Give your answer as a decimal or as a fraction.

More walkthroughs with Fox

Common questions

Which side should I collect x on?

The answer is the same either way. Collect x on the side with the largest x term, so that the number in front of x is positive.

What does it mean if x disappears completely?

If you get something that is never true, like 3 = 7, the equation has no solution. If you get something that is always true, like 5 = 5, every number is a solution.

Can the answer be a negative number or a fraction?

Yes. x = −2 or x = 9/4 is as correct as a whole number. Check by putting the answer in.

Is 3 = x the same as x = 3?

Yes. The equals sign says that the sides are equal, whichever side comes first.

Keep practising with Somokai

Free to start. Hints and explanations when you get stuck.

Start practising for free

Found a mistake? Get in touch

Svenska