Linear Equations and Inequalities

9000024110

Level:

Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ 11x - 2 = 2 - 4x \]

add $(4x + 2)$

multiply by $\frac{1} {11}$

multiply by $\left (-\frac{1} {4}\right )$

add $(-11x + 4x)$

subtract $(4x + 2)$

add $(4x + 2)$

9000024101

Level:

Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ 3x + 2 = -5x + 1 \]

add $(5x - 2)$

multiply by $\frac{1} {3}$

multiply by $-\frac{1} {5}$

add $(-3x + 2)$

add $(5x + 1)$

add $(3x - 1)$

9000021704

Level:

Solve the following inequality. \[ \frac{x + 1} {4} -\frac{x + 2} {3} > \frac{x + 3} {6} -\frac{3x - 4} {12} \]

$x\in \emptyset $

$x\in \mathbb{R}$

$x\in (-\infty ;29)$

$x\in \{0\}$

9000021705

Level:

Solve the following inequality in the set of negative integers. \[ \frac{3x - 4} {2} -\frac{2x - 5} {3} + \frac{3 - 4x} {5} > 0 \]

$x\in \{ - 7;-6;-5;-4;-3;-2;-1\}$

$x\in \emptyset $

$x\in [ - 8;0] $

$x\in \{ - 8;-7;-6;-5;-4;-3;-2;-1\}$

9000021710

Level:

Find the maximal integer $x$ which satisfies the following inequality. \[ \frac{x + 6} {3} -\frac{x - 1} {2} < 2 - 0.2x \]

$- 16$

$- 15$

$- 14$

$14$

9000021702

Level:

Find the positive integer solutions of the following inequality. \[ \frac{1 + x} {3} -\frac{8 - 3x} {2} < \frac{3x} {2} - 2 \]

$x\in \{1;2;3;4\}$

$x\in \mathbb{N}$

$x\in \{1;2;3;4;5\}$

$x\in [ 1;5] $

9000021709

Level:

Find all the values of $x$ for which the expression $\frac{x+5} {4} -\frac{7-3x} {12} $ is not bigger than $\frac{2x+4} {6} + \frac{x-3} {3} $.

$x\in [ 6;\infty )$

$x\in (6;\infty )$

$x\in (-\infty ;6)$

$x\in (-\infty ;6] $

9000021701

Level:

Assume $x\in [ - 2;2] $ and solve the following inequality. \[ 10 + 7x\leq 5 - 3x \]

$x\in \left [ -2;-\frac{1} {2}\right ] $

$x\in \left (-\infty ;-\frac{1} {2}\right ] $

$x\in \left [ -\frac{1} {2};2\right ] $

$x\in [ - 2;2] $

The salary of Peter has been increased by $\$2\: 400$. The salary of Jane increased by $3\, \%$ and this increase has been bigger than the increase of the Peter's salary. In the following list identify a possible old salary of Jane.

$\$81\: 000$

$\$80\: 000$

$\$9\: 000$

$\$8\: 000$

9000018103

Level:

Solve the following inequality assuming positive integer $x$. \[ 1\frac{1} {3}\leq -\frac{x - 4} {2} \]

$x\in \left \{1\right \}$

$x\in \left \{0;1\right \}$

$x\in \left (0; \frac{4} {3}\right ] $

$x\in \emptyset $

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Linear Equations and Inequalities

9000024110

9000024101

9000021704

9000021705

9000021710

9000021702

9000021709

9000021701

9000018010

9000018103

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