Question

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}

Answer 1

Start with the given expression:

`x+2x+6<50`.

Simplify by grouping like terms:

`3x+6<50`

Isolate variable terms:

`3x<44`

Solve for x:

`x<(44)/(3)`

`x<14(2)/(3)`

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

As a check:

`x+2x+6<50`

`14+2(14)+6<50`

`46<50` TRUE

and:

`x+2x+6<50`

`15+2(15)+6<50`

`51<50` FALSE

The only choice that fits is A.