Practice Variable as Placeholder in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A variable acts as a placeholder — a letter or symbol (like x, n, or y) that stands in for an unknown or changing number in a mathematical expression or equation. It represents one specific unknown value that satisfies a given condition.

Like a blank in a sentence: '_+3=7\_ + 3 = 7' asks 'what number fits here?'

Showing a random 20 of 50 problems.

Example 1

challenge
Why is xx in ∫x dx\int x\,dx a 'dummy' placeholder?

Example 2

hard
Solve 2x−35=x+43\dfrac{2x - 3}{5} = \dfrac{x + 4}{3}.

Example 3

hard
A father's age is 33 times his son's age. In 1010 years, the father will be twice as old. Use a variable to find the son's current age.

Example 4

easy
Does the same letter need to stand for the same value within one equation?

Example 5

medium
Two boxes: □+◯=10\square + \bigcirc = 10. Is □\square a single value?

Example 6

medium
Solve for the placeholder: 3(□−2)=93(\square - 2) = 9.

Example 7

easy
Substitute 55 for the placeholder nn in n2n^2.

Example 8

easy
Can the placeholder in 2n=72n = 7 be a fraction?

Example 9

medium
A spreadsheet cell named AA holds a changing total. Placeholder or constant?

Example 10

easy
Find the value of nn in 3n=213n = 21.

Example 11

medium
For how many values of xx is the equation x+5=x+4x + 5 = x + 4 true?

Example 12

medium
Solve x3−4=2\dfrac{x}{3} - 4 = 2.

Example 13

challenge
A two-digit number's tens digit is twice its units digit, and the sum of the digits is 99. Find the number.

Example 14

medium
I think of a number, double it, and add 5 to get 19. What is my number?

Example 15

medium
Solve 3(x−2)=123(x - 2) = 12.

Example 16

medium
In T(n)=2n+1T(n) = 2n + 1, what does the placeholder nn receive?

Example 17

medium
If □×4=△\square \times 4 = \triangle and □=3\square = 3, find △\triangle.

Example 18

easy
In the equation x+8=15x + 8 = 15, what specific value does xx represent?

Example 19

easy
In f(x)=x+2f(x) = x + 2, what role does xx play?

Example 20

easy
Fill the placeholder: □+3=8\square + 3 = 8. What number?
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