Question

for each value of y, determine whether it is a solution to 32 > 4y. (a) is y = 8 a solution? yes no (b) is y = 4 a solution? yes no (c) is y = 11 a solution? yes no (d) is y = 6 a solution? yes no

Explanation:

Step1: Solve the inequality \(32 > 4y\)

Divide both sides by 4: \(\frac{32}{4} > \frac{4y}{4}\), so \(8 > y\) or \(y < 8\).

Step2: Check each value

(a) \(y = 8\)

Since \(y < 8\) is required, \(8\) is not less than \(8\). So not a solution.

(b) \(y = 4\)

\(4 < 8\), so it satisfies \(y < 8\). Solution.

(c) \(y = 11\)

\(11 > 8\), does not satisfy \(y < 8\). Not a solution.

(d) \(y = 6\)

\(6 < 8\), satisfies \(y < 8\). Solution.

Answer:

(a) No
(b) Yes
(c) No
(d) Yes