Representation of Solutions on a Number Line

Q.

Find the point where the graph of the function sgn (x) breaks or becomes discontinuous. ( sgn is the signum function )

Q.

Find the range of values of x, which satisfy :

$-\frac{1}{3}\le \frac{x}{2}+1\frac{2}{3}<5\frac{1}{6}$

Graph, in each of the following cases, the values of x on the different real number lines :

(i) $x\in W$ (ii) $x\in Z$ (iii) $x\in R.$

Q.

Find the square of $105$ using an identity.

Q.

Solutions of which of the inequalities comprising a system in variable x are represented on number lines as given below, (black color is taken in consideration)

1. $x\in [–3,1]$

2. $x\in (–\infty ,–4)\cup (3,\infty )$

3. $x\in [–4,3]$

4. $x\in (–\infty ,–4)\cup [3,\infty )$

Q. Solve the following inequations: $7x+3\ge 3x-5$ and $\frac{x}{4}-5\le \frac{5}{4}-x,xϵR$. Also graph the solution set on the number line.
[4 MARKS]

Q.

For each graph given alongside, write an inequation taking x as the variable :

Q.

Find the correct result, remember that the math is exact.

$$\begin{gathered} 1+4=5 \\ 2+5=12 \\ 3+6=21 \\ 5+8=\_\_\_ \end{gathered}$$

Q. Solve the following inequation : 2y-3 < y+1 $\le$ 4y+7 , where y$\in$R.

1. -2 $\le$ y $\le$ 4
   
2. -2 $<$ y $\le$ 4
3. -2 $\le$ y $<$ 4
4. -2 $<$ y $<$ 4

Q.

The diagram represents two inequations A and B on real number lines :

(i) Write down A and B in set builder notation.

(ii) Represent $A\cap BandA\cap B^{\prime }$ on two different number lines.

Q.

Solve and graph the solution set of :

(i) $3x-2>19or3-2x\ge -7;x\in R.$

(ii) $5>p-1>2or7\le 2p-1\le 17;p\in R.$

Q.

Which of the following number line represent the solution of the inequation: $-8\le 2x<4;x\in \text{R}$?

1. 

2. 

3. 

4. 

Q. Find the vlaues of x, which satisfy the inequation
$-2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2,xϵW$ Graph the solution set on the number line.
[3 MARKS]

Q.

Which of the following number line represents the solution of the inequation: $2y-3<y+2\le 3y+5;y\in \text{R}$?

1. 

2. 

3. 

4. 

Q.

Simplify these expressions and find their values if $x=3,a=-1,b=-2$

$3x-5-x+9$

Q.

Use real number line to find the range of values of x for which :

(i) $x>3and0<x<6.$

(ii) $x<0and-3\le x<1.$

(iii) $-1<x\le 6and-2\le x\le 3$

Q. Solve the following inequation and represent the solution set on the number line:
$-3+x\le \frac{8x}{3}+2\le \frac{14}{3}+2x$, where $xϵI$
[4 MARKS]

Q.

Which of the following represent the solution of the given inequality?

$x^2+2x+5\ge 0\forall x\in R$

1. 

2. 

3. 

4. 

Q.

Solve the inequation :

$3z-5\le z+3<5z-9;z\in R.$

Graph the solution set on the number line.

Q. Which of the following inequations is represented by the the number line below?

1. $0<6x<36;x\in \text{N}$
2. $10<5x<30;x\in \text{N}$
3. $12<6x<36;x\in \text{N}$
4. $0<5x<25;x\in \text{N}$

Q. a) Solve the inequation and represent the solution set on the number line.
$-3+x\le \frac{8x}{3}+2\le \frac{14}{3}+2x,wherexϵI$

b)
Solve the given inequation and graph the solution on the number line
$2y-3<y+1\le 4y+7;yϵR$

[6 MARKS]

Q.

Find the value of sgn(-1) + sgn(0) + sgn(1), where sgn(x) is the signum function

___.

Q.

Find the value of the following expressions, when $x=-1:-x+2$

Q.

Solve the following inequation and represent the solution set on the number line :

$4x-19<\frac{3x}{5}-2\le \frac{-2}{5}+x,x\in R$

Q.

Write the solution set and its representation on the number line for the following inequation.
$\frac{x+1}{3}<15-7x\le -3(x-7);x\in R.$

1. $-1.5\le x<2$
   

2. $-1.5<x<3$
   

3. $-1.5<x<2$
   

4. $-1.5\le x\le 2$
   

Q.

Which is the correct graph of y < x + 2?

1. 

2. 

3. 

4. None of these

Q. Solve the following inequation, write the solution set and represent it on the number line.
$-3(x-7)\ge 15-7x>\frac{x+1}{3},xϵR$
[3 MARKS]

Q.

Given $x\in \left\{realnumbers\right\},\text{find the range of value of x for which}-5\le 2x-3<x+2$ and represent it on a real number line.

Q. Solve the following inequation and represent the solution set on the number line:
$2y-3\le y+1\le 4y+7,yϵR.$
[4 MARKS]

Q.

Is $2$ a complex number?

Q. Which of the following number line represents the solution of the inequation: $x+2>3;x\in \text{N}$?

1. 
2. 
3. 
4.