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?
\( y \geq -\frac32x+\frac{7}2 \)
\( y \leq -\frac32x+\frac{7}2 \)
\( y > -\frac32x+\frac{7}2 \)
\( y < -\frac32x+\frac{7}2 \)