Linear Inequalities, Free Math Test

Problem #1

Which number is a solution to the inequality $3x-2<0$ ?

$\frac{2}{3}$

$\frac{1}{3}$

Problem #2

Which number is not a solution to the inequality $1-6x>0$ ?

- $\frac{1}{3}$

$\frac{1}{3}$

-2

Problem #3

The inequality 4x + 2 > 16 is equivalent to:

$x>-\frac{7}{2}$

$x<3\frac{1}{2}$

$x>3$

$-x<-\frac{7}{2}$

Problem #4

The inequality $3x-7>4x-6$ is equivalent to:

$x>-1$

$5x-1<4x-2$

$4x-1<3x$

$x\leq-1$

Problem #5

The inequality $\frac{x-5}{2}<\frac{5x-4}{3}$ is not equivalent to:

$x+1>0$

$\frac{x}{2}>\frac{x}{3}-\frac{1}{6}$

$3x-1<2x-2$

$1-x>-2x$

Problem #6

The greatest solution to the inequality $5-6x>2(4-x)$ is:

-2

-1

Problem #7

Which is the smallest number that is a solution to the inequality $3.2x-2>2x+0.4$

-2

-3

Problem #8

Which interval is solution to $2x-7<3x+5$

$x\in(-\infty;-12)$

$x\in(-\infty;12)$

$x\in(12;+\infty)$

$x\in(-12;+\infty)$

Problem #9

The solutions to the inequality $\frac{3x-1}{4}<x-1$ are included in:

$x\in(0;+\infty)$

$x\in(-\infty;3)$

$x\in(3;5)$

$x\in(4;+\infty)$

Problem #10

The solution set of inequalities $x-3>1$ and $x+1\leq -1$ is:

$x\in(-4;-2]$

there are no numbers that are solutions of the both inequalities

every $x\in[-2;4)$

evry $x\in(4;+\infty)$

Problem #11

The solution set of both inequalities $\frac{3x-1}{4}<x-1$ and $5(x-\frac{1}{2})+2x-\frac{7}{2}<(x+3.5)\times 3$ is:

$x\in(3;4)$

$x\in(3;\frac{31}{8})$

$x\in(\frac{25}{8};\frac{33}{8})$

$x\in(\frac{17}{8};\frac{33}{8})$

Problem #12

Find all whole positive numbers that are solutions to the inequality $2x-\frac{(x-3)^{2}}{2}\leq 2-\frac{(2x-3)^{2}}{8}$ :

1, 2 and 3

no such numbers

1 and 2

Problem #13

Find all negative whole numbers that are solutions to $\frac{1}{2}-\left ( 2x-\frac{1}{2}(x-3)+\frac{x}{2} \right ).2<0$

-1

the inequality has no negative whole numbers

-1; -2

-2

Problem #14

The solutions to the inequality $\left ( \frac{x}{2}-1 \right )^{2}-\frac{1}{2}\left ( 2-\frac{5x-3}{3} \right )<\frac{x^{2}+1}{4}$ are:

$x\in (-\infty ;-\frac{7}{2})$

$x\in (-4 ;0)$

$x\in (-\frac{9}{2} ;+\infty )$

the inequality has no solutions

Problem #15

The solutions to the inequality $\left ( x-\frac{1}{3} \right )^{2}-\left (-\frac{3}{2}+ \frac{x}{3} \right )^{2}-\frac{1}{3}\left ( -\frac{2}{3}+x \right )<2\left ( \frac{2x}{3}-5 \right )\left ( \frac{2x}{3}+5 \right )-\frac{13}{3}$ are:

$x\in(0;+\infty)$

the inequality has no solutions

$x\in(-\infty;0)$

every number is a solution

Problem #16

The solutions to the inequality $3-\frac{1}{2}\left ( \frac{1}{2}-\frac{2-\frac{x}{3}}{2} \right )>x-\frac{\frac{x}{2}-\frac{3+x}{3}}{2}$ are:

$x<2\frac{3}{4}$

$x<-\frac{33}{12}$

$-x<-2.75$

$x>\frac{33}{12}$

Problem #17

The solutions to the inequality $\frac{1}{5}.\left ( 2-x \right )^{3}+\frac{x^{2}-2x+4}{3}.\left ( -x-2 \right )\leq \frac{x(1-x)(4+x)}{2}-\frac{x^{3}-81x^{2}+32}{30}$ are:

$x\leq 0$

$x\geq 0$

$x\in(0;12)$

$x\in[12;+\infty)$