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:
$x+2x+6$.

Simplify by grouping like terms:
$3x+6$

Isolate variable terms:
$3x$

Solve for x:
$x$
$x$

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

As a check:
$x+2x+6$
$14+2(14)+6$
$46$ TRUE

and:
$x+2x+6$
$15+2(15)+6$
$51$ FALSE

The only choice that fits is A.

Answer 2

Answer:

b

Step-by-step explanation: