Linear Equations in One Variable Test

Result

Linear Equations in One Variable Test - 23

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Solve the equation: $$\dfrac{2z}{1-z}=6$$

A
$$z = \dfrac{1}{4}$$

B
$$z = \dfrac{3}{4}$$

C
$$z = \dfrac{2}{4}$$

D
$$z = \dfrac{3}{7}$$

Solution

Given, $$\dfrac{2z}{1-z}=6$$
On multiplying both sides by $$1 - z$$, we get
$$2z = 6(1 - z)$$
$$2z = 6 - 6z$$
$$8z = 6$$
$$z = \dfrac{3}{4}$$
Question 2
1 / -0

If $$\dfrac {3n}{2} = \dfrac {4n + 3}{3}$$, then $$n =$$?

A
$$6$$

B
$$7$$

C
$$9$$

D
$$11$$

E
$$13$$

Solution

Given, $$\dfrac { 3n }{ 2 } =\dfrac { 4n+3 }{ 3 } $$

$$\Rightarrow 3(3n)=2(4n+3)$$ …[Cross-multiplying the denominators]

$$\Rightarrow 9n=8n+6$$

Transposing $$n$$ terms to one side, we get,
$$\Rightarrow 9n-8n=6$$

$$\Rightarrow n=6$$.

Hence, option $$A$$ is correct.
Question 3
1 / -0

Solve the equation: $$-(x-5)=x-2$$.

A
$$x=\dfrac { 7 }{ 2 } $$

B
$$x=-5$$

C
$$x=3$$

D
$$x=\dfrac{1}{2}$$

Solution

Given, $$-\left( x-5 \right) =x-2$$
$$\implies$$ $$-x+5=x-2$$ ...[By Distribution Law].

Transposing $$x$$ terms to one side, we get,
$$\implies$$ $$x+x=5+2$$
$$\implies$$ $$2x=7$$
$$\implies$$ $$x=\dfrac { 7 }{ 2 } $$.

Hence, option $$A$$ is correct.
Question 4
1 / -0

Solve the equation: $$-2x+6=4x-2$$.

A
no solutions

B
$$0$$

C
$$3$$

D
$$\dfrac {1}{2}$$

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

Solution

Given, $$-2x+6=4x-2$$.

Transposing $$x$$ terms to one side, we get,
$$4x+2x=6+2$$

$$\Rightarrow 6x=8$$

$$\Rightarrow x=\dfrac { 8 }{ 6 } $$

$$\Rightarrow x=\dfrac { 4 }{ 3 } $$.

Hence, option $$E$$ is correct.
Question 5
1 / -0

Three more than twice a integer is equal to $$4$$. What is the integer?

A
$$0.2$$

B
$$0.3$$

C
$$0.4$$

D
$$0.5$$

Solution

Let the number be $$'n'$$
Twice the number gives $$'2n'$$
Three more than twice the number is $$2n+3$$
Given that three more than twice the number $$=$$ $$4$$
$$\Rightarrow 2n$$ $$+$$ $$3$$ $$=$$ $$4$$
$$\Rightarrow 2$$ $$\times$$ $$n$$ $$=$$ $$4$$ $$-$$ $$3$$
$$\Rightarrow n$$ $$=$$ $$\dfrac {1}{2}$$
$$\Rightarrow n$$ $$=$$ $$0.5$$

Therefore, the number is $$0.5$$
Question 6
1 / -0

If $$3$$ times a number is equal to $$\dfrac{3}{2}$$, what is the number?

A
$$\dfrac{1}{3}$$

B
$$\dfrac{1}{2}$$

C
$$\dfrac{2}{3}$$

D
$$2$$

Solution

Let the number be $$'n'$$
Given that $$3$$ times the number $$'n'$$ is equal to $$\dfrac {3}{2}$$
$$\Rightarrow 3$$ $$\times$$ $$n$$ $$=$$ $$\dfrac {3}{2}$$
$$\Rightarrow n$$ $$=$$ $$\dfrac{\frac {3}{2}}{3}$$

$$\Rightarrow n$$ $$=$$ $$\dfrac {3}{6}$$

$$\Rightarrow n$$ $$=$$ $$\dfrac {1}{2}$$
Therefore, the number is $$'$$$$\dfrac {1}{2}$$$$'$$.
Question 7
1 / -0

If $$\dfrac { 1 }{ 7 } +\dfrac { x }{ 7 } =3$$, calculate the value of $$x$$.

A
$$20$$

B
$$7$$

C
$$3$$

D
$$1$$

Solution

Given :- $$\frac{1}{7} + \frac{x}{7} = 3$$
multiplying $$7$$ to both sides
$$\Rightarrow 1+ x = 21$$
$$\Rightarrow x = 21-1$$
$$\Rightarrow x = 20 $$
Question 8
1 / -0

If $$\displaystyle \frac{a-b}{b}=\frac{3}{7}$$, which of the following must also be true?

A
$$\displaystyle \frac{a}{b}=-\frac{4}{7}$$

B
$$\displaystyle \frac{a}{b}=\frac{10}{7}$$

C
$$\displaystyle \frac{a+b}{b}=\frac{10}{7}$$

D
$$\displaystyle \frac{a-2b}{b}=-\frac{11}{7}$$

Solution

Given: $$\displaystyle \frac {a-b}{b}=\frac 37$$
Separating denominators,
$$\Rightarrow \displaystyle \frac ab -1=\frac 37$$
$$\Rightarrow \displaystyle \frac ab=\frac 37+1=\frac {10}{7}$$
$$\Rightarrow \dfrac {a}{b}=\dfrac {10}{7}$$
Therefore, option B is correct.
Question 9
1 / -0

If $$a\neq 0$$ and $$\dfrac{5}{x}=\dfrac{5+a}{x+a}$$, what is the value of $$x$$?

A
$$-5$$

B
$$-1$$

C
$$5$$

D
$$2$$

Solution

Given:
$$a$$ $$\neq$$ $$0$$ and $$\dfrac {5}{x}$$ $$=$$ $$\dfrac {5 \space + \space a}{x \space + \space a}$$
To find the value of $$x$$,
$$\Rightarrow \dfrac {5}{x}$$ $$=$$ $$\dfrac {5 \space + \space a}{x \space + \space a}$$
$$\Rightarrow 5$$ $$\times$$ $$(x$$ $$+$$ $$a)$$ $$=$$ $$x$$ $$\times$$ $$(5$$ $$+$$ $$a)$$
$$\Rightarrow 5x$$ $$+$$ $$5a$$ $$=$$ $$5x$$ $$+$$ $$xa$$
Get the co-efficients of $$'x'$$ on one-side,
$$\Rightarrow 5x$$ $$+$$ $$xa$$ $$-$$ $$5x$$ $$=$$ $$5a$$
$$\Rightarrow xa$$ $$=$$ $$5a$$
As $$(a$$ $$\neq$$ $$0)$$, $$x$$ $$=$$ $$5$$
Therefore, the value of $$'x'$$ is $$'5'$$.
Question 10
1 / -0

Which of the following equations does not have a solution in integers?

A
$$x + 1 = 1$$

B
$$x - 1 = 3$$

C
$$2x + 1 = 6$$

D
$$1 - x = 5$$

Solution

A. $$x+1 = 1$$
$$\implies x= 1 -1 =0$$, which is an integer

B. $$x-1 = 3$$
$$\implies x= 3+1 =4$$, which is an integer

C.$$2x+1 = 6$$
$$\implies 2x= 6-1 =5$$
$$\implies x= \dfrac{5}{2}$$, which is not an integer

D.$$1-x = 5$$
$$\implies -x= 5 -1 =4$$,
$$\implies x=-4$$,which is an integer
$$\therefore$$ Eqn $$2x+1=6$$ does not have solution as an integer

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 23

Result

Linear Equations in One Variable Test - 23

Score

-

Rank

-

SHARING IS CARING

Question 1

$$z = \dfrac{1}{4}$$

$$z = \dfrac{3}{4}$$

$$z = \dfrac{2}{4}$$

$$z = \dfrac{3}{7}$$

Solution

Question 2

$$6$$

$$7$$

$$9$$

$$11$$

$$13$$

Solution

Question 3

$$x=\dfrac { 7 }{ 2 } $$

$$x=-5$$

$$x=3$$

$$x=\dfrac{1}{2}$$

Solution

Question 4

no solutions

$$0$$

$$3$$

$$\dfrac {1}{2}$$

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

Solution

Question 5

$$0.2$$

$$0.3$$

$$0.4$$

$$0.5$$

Solution

Question 6

$$\dfrac{1}{3}$$

$$\dfrac{1}{2}$$

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

$$2$$

Solution

Question 7

$$20$$

$$7$$

$$3$$

$$1$$

Solution

Question 8

$$\displaystyle \frac{a}{b}=-\frac{4}{7}$$

$$\displaystyle \frac{a}{b}=\frac{10}{7}$$

$$\displaystyle \frac{a+b}{b}=\frac{10}{7}$$

$$\displaystyle \frac{a-2b}{b}=-\frac{11}{7}$$

Solution

Question 9

$$-5$$

$$-1$$

$$5$$

$$2$$

Solution

Question 10

$$x + 1 = 1$$

$$x - 1 = 3$$

$$2x + 1 = 6$$

$$1 - x = 5$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.