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Solution - Linear equations with one unknown

Exact form:

x = \frac{25000000}{9}

x=\frac{25000000}{9}

Mixed number form:

x = 2777777 \frac{7}{9}

x=2777777\frac{7}{9}

Decimal form:

x = 2777777.778

x=2777777.778

See steps

Step-by-step explanation

1. Simplify the expression

$1 x + \frac{11}{25} x = 4000000$

Group the coefficients:

$(1 + \frac{11}{25}) x = 4000000$

Convert the integer into a fraction:

$(\frac{25}{25} + \frac{11}{25}) x = 4000000$

Combine the fractions:

$\frac{(25 + 11)}{25} x = 4000000$

Combine the numerators:

$\frac{36}{25} x = 4000000$

2. Isolate the x

$\frac{36}{25} x = 4000000$

Multiply both sides by inverse fraction $\frac{25}{36}$ :

$(\frac{36}{25} x) \cdot \frac{25}{36} = 4000000 \cdot \frac{25}{36}$

Group like terms:

$(\frac{36}{25} \cdot \frac{25}{36}) x = 4000000 \cdot \frac{25}{36}$

Multiply the coefficients:

$\frac{(36 \cdot 25)}{(25 \cdot 36)} x = 4000000 \cdot \frac{25}{36}$

Simplify the fraction:

$x = 4000000 \cdot \frac{25}{36}$

Multiply the fraction(s):

$x = \frac{(4000000 \cdot 25)}{36}$

Simplify the arithmetic:

$x = \frac{25000000}{9}$

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Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

Terms and topics

Linear equations with one unknown