\(Q11.\:\) If \(\frac{x+9}{7} \leq x+3\) , what is the least possible value of \(x\)
\( a) \qquad 2 \)
\( b) \quad -2\)
\(c) \qquad 0 \)
\( d) \qquad 1 \)
\( \text{Answer/Explanation}\)
\(Q12.\:\) If \(\frac{x}{4} -9\leq \frac{x}{3} -11\) , what is the least possible value of \(\frac{2}{8} x\)
\( a) \quad 9 \)
\( b) \quad 8\)
\(c) \quad 7 \)
\( d) \quad 6 \)
\( \text{Answer/Explanation}\)
\(Q13.\:\) If the inequality \(y\geq 2x+3 \) is graphed in the \(xy-plane\), at which point does the boundary line of the inequality intercept the \(x-axis\)?
\( a) \quad \left(2,\frac{3}{2}\right) \)
\( b) \quad \left(0,-\frac{3}{2}\right)\)
\(c) \quad \left(-\frac{3}{2},0\right) \)
\( d) \quad \left(\frac{3}{2},0\right) \)
\( \text{Answer/Explanation}\)
\(Q14.\:\) If \( 3x+3\leq y \leq 2x+5 \) then what is the greatest value of \(x\) is
\( a) \quad 2 \)
\( b) \quad 3\)
\(c) \quad 4\)
\( d) \quad 5\)
\( \text{Answer/Explanation}\)
\(Q15.\:\) If \( \frac{x}{2}+3 \leq y \) and \(\frac{x}{3}+2 \geq y\) then greatest value of \(x\) will be
\( a) \qquad 6\)
\( b) \quad -6\)
\(c) \qquad 0\)
\( d) \qquad 3\)
\( \text{Answer/Explanation}\)
\(Q16.\:\) If the boundary lines of the inequalities \(x+6y≥3\) and \(x−6y \leq 5\) are graphed in the xy-plane, what is their point of intersection?
\( a) \quad\left(0,0\right) \)
\( b) \quad \left(4, -\frac{1}{6}\right) \)
\(c) \quad \left(-\frac{1}{6},4\right)\)
\( d) \quad \left(4, \frac{1}{6}\right) \)
\( \text{Answer/Explanation}\)
\(Q17.\:\) If \(x <y\) and \(y<z\) then which is True?
\( a) \quad x>z\)
\( b) \quad x<z\)
\(c) \quad y>z \)
\( d) \quad y<x\)
\( \text{Answer/Explanation}\)
\(Q18.\:\) If the length of a rectangle is twice its breadth and the minimum area of the rectangle is \(72\), which of the following is NOT true?
\( a) \quad \) The breadth of the rectangle is at least 6.
\( b) \quad \) The length of the rectangle is at least 12.
\(c) \quad \) The minimum perimeter of the rectangle is 36.
\( d) \quad \) The minimum possible value of the length is 6.
\( \text{Answer/Explanation}\)
\(Q19.\:\) Which of the following represents the minimum and maximum possible values for \(x\) given the system of inequalities \(x≥5\) and \(x≤−5\)?
\( a) \quad \) The minimum value is -5, and the maximum value is 5.
\( b) \quad \) The minimum value is 5, and the maximum value is -5.
\(c) \quad \) There is no minimum or maximum value.
\( d) \quad \) The minimum value does not exist, and the maximum value is 5.
\( \text{Answer/Explanation}\)
\(Q20.\:\) Liam is making juice and wants to use twice as much water as lime while ensuring the total amount of juice does not exceed 120 mL. If \(w\) represents the amount of water (in mL) and \(l\) represents the amount of lime (in mL), which of the following inequalities best represents this situation?
\( a) \quad \) \(w+l≤120\) and \(w=2l\)
\( b) \quad \) \(w+l \geq 120\) and \(w=2l\)
\(c) \quad \) \(w+l≤120\) and \(l=2w\)
\( d) \quad \) \(2w+l≤120\)
\( \text{Answer/Explanation}\)