Simple Equations Test

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Simple Equations Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

If $$3x-4=0$$ then $$x$$ is equal to

A
$$ \dfrac{4}{3} $$

B
$$ -\dfrac{2}{3} $$

C
$$ -\dfrac{4}{3} $$

D
$$ -\dfrac{7}{3} $$

Solution

$$3x-4=0$$
Add both side by 4
$$3x-4+4=0+4$$
$$\Rightarrow$$$$3x=4$$
Divide both side by $$3$$

$$\Rightarrow$$$$x=\dfrac 43$$
Question 2
1 / -0

If $$a+5=7$$ find $$a$$

A
$$2$$

B
$$57$$

C
$$75$$

D
None of these

Solution

$$a+5=7$$
Subract both side by 5
$$a+5-5=7-5$$
$$a=2$$
Question 3
1 / -0

If $$2p=34$$ then $$4p =$$ ?

A
$$68$$

B
$$77$$

C
$$91$$

D
$$97$$

Solution

$$2p=34$$
Divide both side by 2
$$\Rightarrow$$$$p=\dfrac{34}2$$

$$\Rightarrow$$$$p=17$$
$$4p=4\times 17=68$$
Question 4
1 / -0

$$x = -1$$ is a solution of the equation

A
$$x - 5 =6$$

B
$$2x + 5 = 7$$

C
$$2(x - 2) + 6 =0$$

D
$$3x + 5 =4$$

Solution

$${\textbf{Step -1: Considering option A.}}$$

$${\text{We have given,}}$$ $$x - 5 = 1$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$ - 1 - 5 = 6$$

$$ \Rightarrow - 6 = 1$$ $${\text{Which is not possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S}} \ne {\text{R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is not a solution of }}x - 5 = 6.$$

$${\textbf{Step -2: Considering option B.}}$$

$${\text{We have given,}}$$ $$2x + 5 = 7$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$2\left( { - 1} \right) + 5 = 7$$

$$ \Rightarrow - 2 + 5 = 7$$

$$ \Rightarrow 3 = 7$$ $${\text{Which is not possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S }} \ne {\text{ R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is not a solution of 2}}x + 5 = 7.$$

$${\textbf{Step -3: Considering option C.}}$$

$${\text{We have given,}}$$ $$2\left( {x - 2} \right) + 6 = 0$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$2\left( { - 1 - 2} \right) + 6 = 0$$

$$ \Rightarrow 2\left( { - 3} \right) + 6 = 0$$

$$ \Rightarrow - 6 + 6 = 0$$

$$ \Rightarrow 0 = 0$$ $${\text{Which is possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S = R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is a solution of 2}}\left( {x - 2} \right) + 6 = 0.$$

$${\textbf{Step -4: Considering option D.}}$$

$${\text{We have given,}}$$ $$3x + 5 = 4$$

$${\text{Putting }}x = - 1{\text{ we get,}}$$

$$3\left( { - 1} \right) + 5 = 4$$

$$ \Rightarrow - 3 + 5 = 4$$

$$ \Rightarrow 2= 4$$ $${\text{Which is not possible}}{\text{.}}$$

$${\text{Here, L}}{\text{.H}}{\text{.S}} \ne {\text{R}}{\text{.H}}{\text{.S }}$$

$${\text{So, - 1 is not a solution of }}3x + 5 = 4.$$

$${\textbf{ Hence, option C}}{\textbf{. 2}}\left(\mathbf {x - 2} \right)\mathbf{ + 6 = 0}{\textbf{ is correct answer.}}$$
Question 5
1 / -0

Which equation among the following don't have $$(-1)$$ as a solution?

A
$$x + 1=0$$

B
$$3x + 4 =1$$

C
$$5x + 7= 2$$

D
$$x -1 =2$$

Solution

$${\textbf{Step -1: Considering option A.}}$$
$${\text{We have given,}}$$ $$x +1 = 0$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$ - 1 +1 = 0$$
$$ \Rightarrow 0 = 0$$ $${\text{Which is possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S}} = {\text{R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is a solution of }}x +1 = 0.$$
$${\textbf{Step -2: Considering option B.}}$$
$${\text{We have given,}}$$ $$3x + 4 = 1$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$3\left( { - 1} \right) + 4 = 1$$
$$ \Rightarrow - 3 + 4 = 1$$
$$ \Rightarrow 1 = 1$$ $${\text{Which is possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S }} = {\text{ R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is a solution of 3}}x + 4 = 1.$$
$${\textbf{Step -3: Considering option C.}}$$
$${\text{We have given,}}$$ $$5x + 7 = 2$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$5\left( { - 1 } \right) + 7 = 2$$
$$ \Rightarrow -5+ 7 = 2$$
$$ \Rightarrow 2 = 2$$ $${\text{Which is possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S = R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is a solution of }}5x+7 =2.$$
$${\textbf{Step -4: Considering option D.}}$$
$${\text{We have given,}}$$ $$x -1 = 2$$
$${\text{Putting }}x = - 1{\text{ we get,}}$$
$$-1-1= 2$$
$$ \Rightarrow - 2 = 2$$ $${\text{Which is not possible}}{\text{.}}$$
$${\text{Here, L}}{\text{.H}}{\text{.S}} \ne {\text{R}}{\text{.H}}{\text{.S }}$$
$${\text{So, - 1 is not a solution of }}x -1 = 2.$$
$${\textbf{ Hence, option D. }}\mathbf{ x-1 =2}{\textbf{ is correct answer.}}$$
Question 6
1 / -0

If $$8x-3=25+17x$$, then $$x$$ is:

A
A fraction

B
An integer

C
A rational number

D
Cannot be solved

Solution

Given, $$8x-3=25+17x$$
$$\Rightarrow 8x-17x=25+3$$ [Transposing $$17x$$ to LHS and $$-3$$ to RHS]
$$\Rightarrow -9x=28$$
$$\therefore x=\dfrac{-28}{9}$$ [Dividing both side by $$-9$$]
Hence, $$x$$ is a rational number.

Therefore, option $$C$$ is correct.
Question 7
1 / -0

What is the method of finding a solution by trying out various values for the variable called?

A
Trial method

B
Trial and error method

C
Substitution method

D
Testing method

Solution
Question 8
1 / -0

Arpita's present age is thrice of Shilpa. If Shilpa's age three years ago was $$x$$. Then Arpita's present age is

A
$$3(x-3)$$

B
$$3x+3$$

C
$$3x-9$$

D
$$3(x+3)$$

Solution
Question 9
1 / -0

If $$\dfrac{x+6}{3} = 7$$, what is the value of $$x$$? ( using trail and error method)

A
$$x= 21$$

B
$$x= 20$$

C
$$x= 15$$

D
$$x= 14$$

Solution

We need to find $$x$$ such that $$\dfrac{x+6}{3}$$ is $$7$$.

We know that $$\dfrac{21}{3}$$ is $$7$$.

We thus get $$7$$ if $$x+6=21$$ $$\Longrightarrow$$ $$x=15$$
Question 10
1 / -0

What value of $$x$$ that makes the following equation true ( using trail and error method) ?
$$\dfrac{x+5}{2} = 3$$

A
$$x = 0$$

B
$$x = 1$$

C
$$x = 2$$

D
$$x = 3$$

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Re-Attempt Weekly Quiz Competition

Simple Equations Test - 19

Result

Simple Equations Test - 19

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SHARING IS CARING

Question 1

$$ \dfrac{4}{3} $$

$$ -\dfrac{2}{3} $$

$$ -\dfrac{4}{3} $$

$$ -\dfrac{7}{3} $$

Solution

Question 2

$$2$$

$$57$$

$$75$$

None of these

Solution

Question 3

$$68$$

$$77$$

$$91$$

$$97$$

Solution

Question 4

$$x - 5 =6$$

$$2x + 5 = 7$$

$$2(x - 2) + 6 =0$$

$$3x + 5 =4$$

Solution

Question 5

$$x + 1=0$$

$$3x + 4 =1$$

$$5x + 7= 2$$

$$x -1 =2$$

Solution

Question 6

A fraction

An integer

A rational number

Cannot be solved

Solution

Question 7

Trial method

Trial and error method

Substitution method

Testing method

Solution

Question 8

$$3(x-3)$$

$$3x+3$$

$$3x-9$$

$$3(x+3)$$

Solution

Question 9

$$x= 21$$

$$x= 20$$

$$x= 15$$

$$x= 14$$

Solution

Question 10

$$x = 0$$

$$x = 1$$

$$x = 2$$

$$x = 3$$

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