Question

Which inequalities have $-0.5$, $2.5$, and $4$ as part of the solution set? Select all that apply.

• A. $z>-3$
• B. $z<5$
• C. $z<4$
• D. $z\le 4$
• E. $z>0$

Answer 1

Answer: (A), (B), (D)

$z\le 4$

Explanation for correct option:

Option(A):

Substitute $-0.5$, $2.5$, and $4$ separately for $z$ in the inequality $z>-3$ .

$-0.5>-3$

$-2.5>-3$

$4>-3$

All these inequations are true.

Therefore, option (A) is correct option.

Option(B):

Now, substitute $-0.5$, $2.5$, and $4$ separately for $z$ in the inequality $z<5$.

$-0.5<5$

$-2.5<5$

$4<5$

All these equations are true.

Therefore, option (B) is correct option.

Option(D):

Substitute $-0.5$, $2.5$, and $4$ separately for $z$ in the inequality $z\le 4$ .

$-0.5⩽4$

$-2.5⩽4$

$4⩽4$

All these equations are true.

Therefore, option (D) is correct option.

Explanation for incorrect option:

Option(C):

Substitute $-0.5$, $2.5$, and $4$ separately for $z$ in the inequality $z<4$.

$-0.5<4$

$-2.5<4$

$4\nless 4$

Since $z=4$ does not satisfy the equation $z<4$.

Therefore, option (C) is not correct option.

Option(E):

Now substitute $-0.5$, $2.5$, and $4$ separately for $z$ in the inequality $z>0$ .

$-0.5\ngtr 0$

$-2.5\ngtr 0$

$4>0$

Since $z=-0.5$ and $z=-2.5$ does not satisfy the equation $z>0$.

Therefore, option (E) is not correct option.

Hence, option (A), (B) and (D) are correct options.