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Lesson · Grade 7 · Mathematics

Two-step equations on a balance

  • Grade 7
  • Mathematics
  • 1 min 9 s
  • British Columbia
  • BC7-MA-42

A balance with three x boxes and 4 blocks against 16 blocks shows how to solve 3x + 4 = 16: take 4 blocks off both sides to get 3x = 12, then split each side into 3 equal groups to find x = 4. The working beside it writes − 4 and ÷ 3 under both sides, checks that 3 × 4 + 4 = 16, and ends with the recap: subtract first, then divide, on both sides.

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In one sentence

The question this lesson answers

Let us solve the equation 3x plus 4 equals 16.

An equation is like a balance, with equal amounts on both sides.

Transcript

What the lesson says

Let us solve the equation 3x plus 4 equals 16.

An equation is like a balance, with equal amounts on both sides.

The left side holds three x boxes and four blocks.

The right side holds sixteen blocks.

We want to find how many blocks one x box is worth.

First, take the four loose blocks off the left side.

Now the right side is heavier, so the scale tips.

Take four blocks off the right side too, and the scale is level again.

Now three x boxes balance twelve blocks, so 3x equals 12.

Next, split each side into three equal groups.

Each x box matches a group of four blocks.

One x box balances four blocks, so x equals 4.

Check it: 3 times 4 is 12, and 12 plus 4 is 16.

Undo the adding first, then the multiplying, doing the same to both sides.

Curriculum

Where this fits

British Columbia, Grade 7

Mathematics, Patterns and algebra: two-step equations with whole-number coefficients, constants, and solutionsBC7-MA-42

Previous: Solving One-Step EquationsNext: Two-Step Equations: Undo Each Step

The outcomes and strands follow the British Columbia curriculum.

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