# How do I solve 3x 1 82

## Equations with an unknown When solving a calibration with an unknown (a, b, ... n, m ... x, y ...) the point is to find out the value of these unknowns.

Here you can ...

### Brain Teasers: Playing with Equations

Exercise 1: Click on an example letter and calculate the exercise. Can you figure out the trick?

### Solve equations (equivalence transformations)

When solving a calibration with an unknown (x) is about this unknown (x) to find out. As a trick, imagine an equation as a scale. The "weight" of both scales is changed so that in the end only x is on one pan and the solution number is on the other. If the balance is in equilibrium at that moment, you have the solution.

example

### Simple equations

Exercise 3: Calculate the length of the sides x and y.

Exercise 4: Enter the correct values.

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Exercise 5: Compute x from -x.

If -x appears as the result of an equation, the question arises: "How do you get from -x to x?" One possibility is to multiply both sides of the equation by (-1).

Examples:

 -x = 5 | · (-1) -x (-1) = 5 · (-1) x = -5

 -x = -5 | · (-1) -x (-1) = - 5 · (-1) x = 5

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Exercise 7: Click on whether the x in the red term corresponds to ¼, ½ or ¾. Nine terms are to be assigned.

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Exercise 8: Equilibrate the scale shown below by entering the appropriate value for y. correct: 0 incorrect: 0

Exercise 9: Calculate the length of a section x.

x = cm

x = cm

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Exercise 10: Enter the correct values.

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Exercise 11: Compute x

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Exercise 12: Calculate the length of the line x.

Specification in cm

x: a = b cm

x = cm

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Exercise 13: Calculate the length of the line x.

Specification in cm

x: a * b = c cm

x = cm

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Exercise 14: Compute x

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Exercise 15: Compute x

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Exercise 16: Calculate the length of a section x.

x + cm = cm

cm - x = cm

x = cm

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Exercise 18: Compute x

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Exercise 19: Compute x

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Exercise 20: Compute x

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Exercise 21: Compute x

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Exercise 22: Compute x

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Exercise 23: Compute x

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Exercise 24: Compute x

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Exercise 25: Enter the numbers in the text fields with which both sides of the lower scale should be changed. Click on "Go" to make the change.

Exercise 26: Calculate the length of a section x.

x + cm = x + cm

x = cm

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Exercise 27: Compute x

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Exercise 28: Compute x

x =

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Exercise 29: Compute x

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Exercise 30: Compute x

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### Equations with parentheses

Reshaping

Equations are solved by transforming them. In the end, the variable stands alone on one side and the solution on the other side of the equal sign.

May be on both sides of the equation

• the same number can be added or multiplied.
• multiplied by or divided by the same number (other than 0).
During conversion, a line on the edge of the calculation (|) shows which arithmetic operations were carried out on both sides of the equation.

example

 a) Dissolve the bracketb) Summarize 2y - (2 + 4y) 2y - 2 - 4y = = 32 - 2 (4y - 4) 32 - 8y + 8 | Ka | zf c) One-sided variable d) variable alone e) Calculate the variable -2 - 2y -2 + 6y 6y y = = = = -8y + 40 40 42 7 | + 8y | +2 | :6

Exercise 31: Click on the desired exercise type in the drop-down menu. Calculate the term marked in color and insert the solution into the text field of the same color.

Exercise 32: Compute x

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Exercise 33: Compute x

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Exercise 34: Compute x

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Exercise 35: Compute x

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Exercise 36: Compute x

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Exercise 37: Compute x

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Exercise 38: Compute x

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Exercise 39: Compute x

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### Word problems with technical terms

Exercise 40: Set up an equation for the text and calculate x.

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Exercise 41: Enter the correct values ​​for the unknowns (v, w, x, y, z).

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Exercise 42: a number x, you get that from x.

x =

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Exercise 43: Decreased by that of a number x, you get again x.

x =

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x =

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Exercise 45: The third part of a number is 2 larger than the fourth part.

It's the number.

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Exercise 46: Set up an equation for the text and calculate x.