Question

Which number line shows the solution set for StartAbsoluteValue StartFraction s Over 2 EndFraction + 4 EndAbsoluteValue less-than 2.? A number line going from negative 14 to positive 10. Open circles are at negative 12 and negative 4. Everything between the points is shaded. A number line going from negative 14 to positive 10. Open circles are at negative 12 and negative 4. Everything to the left of negative 12 and to the right of negative 4 is shaded. A number line going from negative 14 to positive 10. Closed circles are at negative 4 and positive 4. Everything to the left of negative 4 and to the right of positive 4 is shaded. A number line going from negative 14 to positive 10. Closed circles are at negative 4 and positive 4. Everything between the points is shaded.

Answer 1

The solution set for |s/2 + 4| < 2 is all the values of 's' between -12 and -4, not including the endpoints. This is depicted on a number line as a shaded region between open circles at -12 and -4.

Step-by-step explanation:

We are given the inequality |\frac{s}{2} + 4| < 2. To find the solution set, we first consider the absolute value expression without the inequality, which is split into two equations because absolute value represents the distance from zero: one for when the expression inside is positive (\(\frac{s}{2} + 4 = 2\)) and one for when it is negative (\(\frac{s}{2} + 4 = -2\)).

Solve these two equations:

\(\frac{s}{2} + 4 = 2\) leads to \(\frac{s}{2} = -2\) and then \(s = -4\).

\(\frac{s}{2} + 4 = -2\) leads to \(\frac{s}{2} = -6\) and then \(s = -12\).

The solution set of the inequality is all values of 's' between -12 and -4. On a number line, this is represented with open circles at -12 and -4, with the space between them shaded, as the inequality is strict (<) and does not include the endpoints.

The correct number line is the one going from negative 14 to positive 10 with open circles at negative 12 and negative 4 with everything between the points shaded.

Answer 2

GRAPH C

Step-by-step explanation: