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fredd [130]
2 years ago
7

Seven times the opposite of a number is 50 less than 3 times the number. What is the number?

Mathematics
2 answers:
Kazeer [188]2 years ago
8 0

<u>Question</u> :-

  • Seven times the opposite of a number is 50 less than 3 times the number. What is the number?

<u>Explanation</u> :-

  • Let the number be " x. "

According to the question, it's given –

Seven times the opposite of a number is 50 less than 3 times the number.

We've assumed that the number is x. So, opposite of the number will be -x.

\qquad\pink{ \bf  \longrightarrow 7(-x) = 3x-50}

Now, let's solve this equation –

\qquad\bf  \longrightarrow 7(-x) = 3x-50

\qquad\sf  \longrightarrow -7x = 3x -50

Subtract 3x from both side –

\qquad\sf  \longrightarrow -7x -3x = 3x -50-3x

Cancel 3x from right side –

\qquad\sf  \longrightarrow -7x -3x =\cancel{ 3x} -50-\cancel{3x }

\qquad\sf  \longrightarrow -10x = -50

Now, cancel (-) sign from both side –

\qquad\sf  \longrightarrow \cancel{-}10x = \cancel{-}50

\qquad\sf  \longrightarrow 10 x = 50

Then, divide both sides by 10 –

\qquad\sf  \longrightarrow \dfrac{10x}{10} = \dfrac{50}{10}

\qquad\sf  \longrightarrow \dfrac{\cancel{10}x}{\cancel{10}} = \cancel{\dfrac{50}{10}}

\qquad\pink{ \bf  \longrightarrow x = 5 }

  • Henceforth, the number will be 5.
almond37 [142]2 years ago
6 0

Answer: The number is 5

Creating an Equation:

      First, we will need to write a mathematical equation that represents the problem.

-> If <em>n</em> is our number, then the opposite of <em>n</em> is -<em>n</em> because -1 times -n is n and -1 times n is -n

-> The underlined portion becomes a part of our equation in the next line.

<u>Seven times the opposite of a number</u> is 50 less than <u>3 times the number</u>

7 * -<em>n</em> is <u>50 less than 3</u><u><em>n</em></u><u> </u>

7 * -<em>n</em> <u>is</u> 3<em>n</em> - 50

7(-<em>n) </em>= 3<em>n</em> - 50

Solving for the Number:

7(-<em>n) </em>= 3<em>n</em> - 50     =|=     Our equation

-7<em>n</em> = 3<em>n</em> - 50       =|=     Distribute the 7 into -<em>n</em>

-10<em>n</em> = -50            =|=     Subtract 3<em>n</em> from both sides of the equation

n = 5                     =|=     Divide both sides of the equation by -10

Our number is <u>5</u>

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