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Question :-

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

Explanation :-

  • 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.

[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow 7(-x) = 3x-50} [/tex]

Now, let's solve this equation –

[tex]\qquad[/tex][tex] \bf \longrightarrow 7(-x) = 3x-50 [/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow -7x = 3x -50[/tex]

Subtract 3x from both side –

[tex]\qquad[/tex][tex] \sf \longrightarrow -7x -3x = 3x -50-3x [/tex]

Cancel 3x from right side –

[tex]\qquad[/tex][tex] \sf \longrightarrow -7x -3x =\cancel{ 3x} -50-\cancel{3x }[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow -10x = -50[/tex]

Now, cancel (-) sign from both side –

[tex]\qquad[/tex][tex] \sf \longrightarrow \cancel{-}10x = \cancel{-}50[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 10 x = 50[/tex]

Then, divide both sides by 10 –

[tex]\qquad[/tex][tex] \sf \longrightarrow \dfrac{10x}{10} = \dfrac{50}{10}[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow \dfrac{\cancel{10}x}{\cancel{10}} = \cancel{\dfrac{50}{10}}[/tex]

[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow x = 5 }[/tex]

  • Henceforth, the number will be 5.
Heather

Answer: The number is 5

Creating an Equation:

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

-> If n is our number, then the opposite of n is -n 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.

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

7 * -n is 50 less than 3n

7 * -n is 3n - 50

7(-n) = 3n - 50

Solving for the Number:

7(-n) = 3n - 50     =|=     Our equation

-7n = 3n - 50       =|=     Distribute the 7 into -n

-10n = -50            =|=     Subtract 3n from both sides of the equation

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

Our number is 5

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