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Lesson · Grade 9 · Mathematics

Equations with the variable on both sides

  • Grade 9
  • Mathematics
  • 2 min 14 s
  • British Columbia
  • BC9-MA-20

A balance of blue x blocks and gold unit cubes solves 5x + 3 = 2x + 15 one step at a time: take 2x off both sides, then 3, then split both sides into 3 equal groups, so x = 4. Both sides come to 23 in the check. The same steps then solve 2x + 9 = 5x + 18 to get x = −3, the video shows the common mistake of moving a term across without changing its sign, and it ends on a one-line recap.

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In one sentence

The question this lesson answers

How do we solve 5x plus 3 equals 2x plus 15, when x is on both sides?

Here, x is the variable, a letter that stands for an unknown number.

Transcript

What the lesson says

How do we solve 5x plus 3 equals 2x plus 15, when x is on both sides?

Here, x is the variable, a letter that stands for an unknown number.

Picture a balance. Each blue block is one x, and each gold cube is 1.

The left side holds 5x plus 3, and the right side holds 2x plus 15.

Both sides are equal, so to keep the balance level, do the same to both sides.

First, take 2x off both sides. That leaves 3x plus 3 equals 15.

Next, take 3 off both sides. Now 3x equals 12.

Divide both sides by 3, splitting each side into 3 equal groups.

One x balances 4 cubes, so x equals 4.

Check by putting 4 in place of x in the first equation.

The left side is 5 times 4 plus 3, which is 23.

The right side is 2 times 4 plus 15, also 23, so x equals 4 is correct.

The same steps solve 2x plus 9 equals 5x plus 18.

Take 2x off both sides: 9 equals 3x plus 18. Take 18 off both sides: negative 9 equals 3x.

Divide both sides by 3: negative 3 equals x, so x equals negative 3.

Check: 2 times negative 3 plus 9 is 3, and 5 times negative 3 plus 18 is 3.

A common mistake is moving a term, like 2x, to the other side without changing its sign.

Taking 2x off both sides gives 5x minus 2x: plus 2x on the right becomes minus 2x on the left.

To recap: do the same to both sides until x is alone, then check your answer.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: multi-step one-variable linear equationsBC9-MA-20

Previous: Solving Equations with Brackets and Like TermsNext: Equations with Fractions: Solve and Check

The outcomes and strands follow the British Columbia curriculum.

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