Systems of Linear Equations and Inequalities

2000017705

Level: 
C
The interval \( \left[ -\frac{12}{11}, \frac6{23}\right)\) is the solution of a system of two linear inequalities with one unknown. Which of the following systems is it?
\(\begin{aligned} \frac{x}3-\frac{x}4 &> 2x-\frac12 \\ 3x+8 &\geq 2-\frac52x \end{aligned}\)
\(\begin{aligned} \frac{x}3-\frac{x}4 &\geq 2x-\frac12\\ 3x+8 &> 2-\frac52x \end{aligned}\)
\(\begin{aligned} \frac{x}3-\frac{x}4& < 2x-\frac12 \\ 3x+8 &\geq 2-\frac52x \end{aligned}\)
\(\begin{aligned} \frac{x}3-\frac{x}4 &> 2x-\frac12 \\ 3x+8 &\leq 2-\frac52x \end{aligned}\)

2000017706

Level: 
C
Which of the systems has its solution graphed on the number line?
\(\begin{aligned} -5x-4 &>11-2x \\ 8-9x &> 2x-69 \end{aligned}\)
\(\begin{aligned} -5x-4 &>11-2x \\ 8-9x& < 2x-69 \end{aligned}\)
\(\begin{aligned} -5x-4 &< 11-2x\\ 8-9x &< 2x-69 \end{aligned}\)
\(\begin{aligned} -5x-4& < 11-2x\\ 8-9x &> 2x-69 \end{aligned}\)

2010011201

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which inequality is it?
\( y \geq -\frac32x+\frac{7}2 \)
\( y \leq -\frac32x+\frac{7}2 \)
\( y > -\frac32x+\frac{7}2 \)
\( y < -\frac32x+\frac{7}2 \)

9000021801

Level: 
C
Solve the following system of inequalities. \[\begin{aligned} \frac{1} {3}(2x + 5) &\geq 0.5\left (\frac{2 + 3x} {2} + 2\right ) & & \\0.2(3 - 2x) &\leq \frac{1} {3}\left (\frac{4 - 2x} {5} + 2\right ) & & \end{aligned}\]
\(x\in \left [ -\frac{5} {4},2\right ] \)
\(x\in [ 2,\infty )\)
\(x\in \left (-\infty ,-\frac{5} {4}\right ] \)
\(x\in \emptyset \)