EN
BuilderGrade 7⏱ 15 min

Equations as a balance

Solve equations on a balance scale: whatever you do to one side, do to the other.

Standards: 7.EE.B.46.EE.B.7

1Wonder

Two mystery bags and 3 blocks weigh exactly the same as 11 blocks. How much does one bag weigh, without opening it?

2Explore

Balance scale

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Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.

2x + 3 = 11xxSillyChili
Steps: 2x + 3 = 11
Try this
  • Solve the first puzzle using only moves that keep the scale balanced.
  • Press Take 1 block from the left only. What happens to the scale and the equation? Then Undo.
  • Try the puzzles with x on both sides. Which move do you need first?
  • When you finish, open the bags to check your answer.

3Explain

2x + 3 = 11xxSillyChili
Step 1 of 5

An equation is a balance

The equal sign means both sides weigh the same. 2x + 3 = 11: two bags and 3 blocks balance 11 blocks.

The golden rule

Whatever you do to one side of an equation, do the same to the other side. Then undo the operations one at a time:

2x+3=11  →−3  2x=8  →÷2  x=42x + 3 = 11 \;\xrightarrow{-3}\; 2x = 8 \;\xrightarrow{\div 2}\; x = 4

4Practice

Question 1 of 5

Solve x + 7 = 12.

5Recap

  • An equation is like a balanced scale: both sides are equal.
  • To keep it balanced, do the same thing to both sides.
  • Undo the operations one by one (usually: + or − first, then × or ÷).
  • Check by putting your answer back into the original equation.