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Solve for x. 12 x-39 <= 9quad AND quad-4x+3 < -6 Choose 1 answer: (A) x >= 4 (B) (9)/(4) < x <= 4 (C) x > -(9)/(4) (D) There are no solutions (E) All values of x are solutions

Solve for x x .\newline12x−39≤9 12 x-39 \leq 9 \quad AND \quad-4 x+3<-6 \newlineChoose 11 answer:\newline(A) x≥4 x \geq 4 \newline(B) 94<x4=""≤="" \frac{9}{4}<x 4="" \leq="" \newline(c)="" =""x="">−94="" x="">-\frac{9}{4} \newline(D) There are no solutions\newline(E) All values of x x are solutions

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Q. Solve for x x .\newline12x−39≤9 12 x-39 \leq 9 \quad AND −4x+3<−6 \quad-4 x+3<-6 \newlineChoose 11 answer:\newline(A) x≥4 x \geq 4 \newline(B) 94<x≤4 \frac{9}{4}<x \leq 4 \newline(C) x>−94 x>-\frac{9}{4} \newline(D) There are no solutions\newline(E) All values of x x are solutions
  1. Solve First Inequality: First, let's solve the inequality 12x−39≤912x - 39 \leq 9. Add 3939 to both sides to isolate the term with xx. 12x−39+39≤9+3912x - 39 + 39 \leq 9 + 39 12x≤4812x \leq 48
  2. Solve Second Inequality: Now, divide both sides by 1212 to solve for xx.12x12≤4812\frac{12x}{12} \leq \frac{48}{12}x≤4x \leq 4
  3. Combine Inequalities: Next, let's solve the inequality -4x + 3 < -6.\newlineSubtract 33 from both sides to isolate the term with xx.\newline-4x + 3 - 3 < -6 - 3\newline-4x < -9
  4. Combine Inequalities: Next, let's solve the inequality -4x + 3 < -6.\newlineSubtract 33 from both sides to isolate the term with xx.\newline-4x + 3 - 3 < -6 - 3\newline-4x < -9Now, divide both sides by −4-4, remembering to flip the inequality sign because we're dividing by a negative number.\newline-4x / -4 > -9 / -4\newlinex > 9/4
  5. Combine Inequalities: Next, let's solve the inequality -4x + 3 < -6.\newlineSubtract 33 from both sides to isolate the term with xx.\newline-4x + 3 - 3 < -6 - 3\newline-4x < -9Now, divide both sides by −4-4, remembering to flip the inequality sign because we're dividing by a negative number.\newline-4x / -4 > -9 / -4\newlinex > 9/4Combine the two inequalities to find the range for xx.\newline9/4 < x \leq 4

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