MAX125
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A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number.
From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are

A: {13, 14}

B: {13, 14, 15}

C: {15, 16, 17}

D: {16, 17}

Respuesta :

twvogels
Start with the given expression:
[tex]x+2x+6<50[/tex].

Simplify by grouping like terms:
[tex]3x+6<50[/tex]

Isolate variable terms:
[tex]3x<44[/tex]

Solve for x:
[tex]x<\frac{44}{3}[/tex]
[tex]x<14\frac{2}{3}[/tex]

Therefor the expression holds for integers less than or equal to 14.

As a check:
[tex]x+2x+6<50[/tex]
[tex]14+2(14)+6<50[/tex]
[tex]46<50[/tex] TRUE

and:
[tex]x+2x+6<50[/tex]
[tex]15+2(15)+6<50[/tex]
[tex]51<50[/tex] FALSE

The only choice that fits is A.

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