Three less then 3 times a number is equal to 23 less than half the number.

(a) Translate the sentence into an equation.
(b) Solve the equation. Show your work.

Respuesta :

frika

Let x be a number. Then:

  • 3 times a number is 3x;
  • Three less then 3 times a number is 3-3x;
  • half the number is [tex]\dfrac{1}{2}x;[/tex]
  • 23 less than half the number is [tex]23-\dfrac{1}{2}x.[/tex]

(a) Thus, the equation is

[tex]3-3x=23-\dfrac{1}{2}x.[/tex]

(b) Multiply this equation by 2:

[tex]6-6x=46-x,\\\\-6x+x=46-6,\\\\-5x=40,\\\\5x=-40,\\\\x=-8.[/tex]


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