If (3)/(4)x+2 <= 11, what is the greatest possible value of (3)/(4)x-9 ? Choose 1 answer: (A) -(9)/(4) (B) 0 (c) 9 (D) 12

Solve Inequality: First, let's solve the inequality (3/4)x + 2 ≤ 11 to find the maximum value of x. Subtract 2 from both sides of the inequality to isolate the term with x. (3/4)x + 2 - 2 ≤ 11 - 2 (3/4)x ≤ 9Divide by Reciprocal: Now, divide both sides of the inequality by (3/4) to solve for x. To do this, multiply both sides by the reciprocal of (3/4), which is (4/3). (4/3) * (3/4)x ≤ (4/3) * 9 x ≤ 12Substitute x = 12: We have found that x is less than or equal to 12. Now we need to find the greatest possible value of (3/4)x - 9. Substitute x = 12 into the expression (3/4)x - 9 to find the maximum value. (3/4)(12) - 9Calculate Value: Calculate the value of (3/4)(12) - 9. (3/4)(12) = 3 * 3 - 9 9 - 9 = 0Find Maximum Value: The greatest possible value of (3/4)x - 9, when x is less than or equal to 12, is 0. Therefore, the correct answer is (B) 0.

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If
(3)/(4)x+2 <= 11, what is the greatest possible value of
(3)/(4)x-9 ?
Choose 1 answer:
(A)
-(9)/(4)
(B) 0
(c) 9
(D) 12

If $\frac{3}{4} x+2 \leq 11$ , what is the greatest possible value of $\frac{3}{4} x-9$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{9}{4}$ $\newline$ (B) $0$ $\newline$ (C) $9$ $\newline$ (D) $12$

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Full solution

Q. If

\frac{3}{4} x+2 \leq 11

, what is the greatest possible value of

\frac{3}{4} x-9

\newline

Choose

1

answer:

\newline

(A)

-\frac{9}{4}

\newline

(B)

0

\newline

(C)

9

\newline

(D)

12

Solve Inequality: First, let's solve the inequality $(\frac{3}{4})x + 2 \leq 11$ to find the maximum value of $x$ . $\newline$ Subtract $2$ from both sides of the inequality to isolate the term with $x$ . $\newline$ $(\frac{3}{4})x + 2 - 2 \leq 11 - 2$ $\newline$ $(\frac{3}{4})x \leq 9$
Divide by Reciprocal: Now, divide both sides of the inequality by $(\frac{3}{4})$ to solve for $x$ . $\newline$ To do this, multiply both sides by the reciprocal of $(\frac{3}{4})$ , which is $(\frac{4}{3})$ . $(\frac{4}{3}) \times (\frac{3}{4})x \leq (\frac{4}{3}) \times 9$ $\newline$ $x \leq 12$
Substitute $x = 12$ : We have found that $x$ is less than or equal to $12$ . Now we need to find the greatest possible value of $\frac{3}{4}x - 9$ . $\newline$ Substitute $x = 12$ into the expression $\frac{3}{4}x - 9$ to find the maximum value. $\newline$ $\frac{3}{4}(12) - 9$
Simplify Further: Calculate the value of $(\frac{3}{4})(12) - 9$ . $\newline$ $= 3 \times 3 - 9$ $\newline$ $=9 - 9$ $\newline$ $= 0$
Find Maximum Value: The greatest possible value of $(\frac{3}{4})x - 9$ , when $x$ is less than or equal to $12$ , is $0$ . $\newline$ Therefore, the correct answer is (B) $0$ .