Hanger Diagrams Worksheet – Find x on Each Hanger

All 12 hangers on the diagram

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What is x? 9

x = 5 Take 4 off both sides: x = 5.
x = 2 Take 5 off both sides: x = 2.
x = 4 Two equal weights make 8: x = 4.
x = 6 Three equal weights make 18: x = 6.
x = 3 Take 1 off both sides: 2x = 6, so x = 3.
x = 8 Take 4 off both sides: 2x = 16, so x = 8.
x = 7 Take x off both sides: 2x = 14, so x = 7.
x = 9 Take x and 6 off both sides: x = 9.
x = 10 Take x off both sides: 2x = 20, so x = 10.

Which equation? 3

2x + 3 = 25 Left: two x and 3. Right: 25.
2x + 3 = x + 25 Left: two x and 3. Right: one x and 25.
2x = x + 25 Left: two x. Right: one x and 25.

How this list was compiled: Own work: the twelve hangers and their numbers are the site's, and none is taken from a published sheet. The idea was read on 2026-10-03 in two places. (1) Wikipedia, English edition, Equation, https://en.wikipedia.org/wiki/Equation: an equation is like a weighing scale or balance, each side of the equation one side of the balance; if an amount is removed from one pan, the same amount must come off the other to keep the scale in balance; an equation stays balanced when each side gets the same operation. (2) An openly licensed grade 6 mathematics course, lesson Staying in Balance, https://im.kendallhunt.com/MS/students/1/6/3/index.html: a hanger balances when its two sides weigh the same, and keeps its balance if the same change is made to both; each piece is labeled with its weight. No answer is typed by hand: every hanger is solved by the program that draws it, and again by a second program. Licence: own work

The drawing: Drawn for this site on 2026-10-03 by script from the answer table in the dataset. Own work. Licence: own work

How it works

This hanger diagram worksheet shows twelve balanced hangers. A triangle marked x is an unknown weight, and a round weight carries its number. Find x on the first nine, then name the equation each of the last three shows.

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Read a hanger as an equation

A hanger hangs level when both sides weigh the same, so the level bar works like an equals sign. One x and a 4 on the left with a 9 on the right is x + 4 = 9.

Find x

Take the same weight off both sides and the hanger stays level. Take 4 off each side of x + 4 = 9, and x = 5 is left. When x hangs on both sides, take one x off each side first.

Questions and answers

What is a hanger diagram in math?

A picture of a balanced hanger with weights on its two sides. It stands for an equation: the weights on the left equal the weights on the right, and a shape with a letter is an unknown weight.

How do you solve a hanger diagram?

Change both sides in the same way until one x is alone. For two x and a 1 balancing a 7, take 1 off each side to get 2x = 6, then halve both sides: x = 3.

How do you write an equation from a hanger diagram?

Add up what hangs on the left, write an equals sign for the level bar, then add up the right. Two x and a 3 on the left with a 25 on the right is 2x + 3 = 25.

Does the worksheet come with answers?

Yes. Print the answer key gives the numbered sheet with the answer for every hanger listed under it. On screen, Quiz yourself on this worksheet checks each answer as you give it.