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Solution - Linear equations with one unknown

c = 3

c=3

See steps

Step-by-step explanation

1. Simplify the expression

$0.2 \cdot (10 - 5 c) = 5 c - 16$

Expand the parentheses:

$0.2 \cdot 10 + 0.2 \cdot - 5 c = 5 c - 16$

Simplify the arithmetic:

$2 + 0.2 \cdot - 5 c = 5 c - 16$

Multiply the coefficients:

$2 - 1 c = 5 c - 16$

Combine like terms:

$2 - c = 5 c - 16$

2. Group all c terms on the left side of the equation

$2 - c = 5 c - 16$

Subtract $5 c$ from both sides:

$(2 - c) - 5 c = (5 c - 16) - 5 c$

Group like terms:

$(- c - 5 c) + 2 = (5 c - 16) - 5 c$

Simplify the arithmetic:

$- 6 c + 2 = (5 c - 16) - 5 c$

Group like terms:

$- 6 c + 2 = (5 c - 5 c) - 16$

Simplify the arithmetic:

$- 6 c + 2 = - 16$

3. Group all constants on the right side of the equation

$- 6 c + 2 = - 16$

Subtract $2$ from both sides:

$(- 6 c + 2) - 2 = - 16 - 2$

Simplify the arithmetic:

$- 6 c = - 16 - 2$

Simplify the arithmetic:

$- 6 c = - 18$

4. Isolate the c

$- 6 c = - 18$

Divide both sides by -6:

$\frac{(- 6 c)}{- 6} = \frac{- 18}{- 6}$

Cancel out the negatives:

$\frac{6 c}{6} = \frac{- 18}{- 6}$

Simplify the fraction:

$c = \frac{- 18}{- 6}$

Cancel out the negatives:

$c = \frac{18}{6}$

Find the greatest common factor of the numerator and denominator:

$c = \frac{(3 \cdot 6)}{(1 \cdot 6)}$

Factor out and cancel the greatest common factor:

$c = 3$

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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

Solution - Linear equations with one unknown

Step-by-step explanation

1. Simplify the expression

2. Group all c terms on the left side of the equation

3. Group all constants on the right side of the equation

4. Isolate the c

Why learn this

Terms and topics

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