Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

Solve the equation:
$$\displaystyle\frac { x-5 }{ 7 } =\displaystyle\frac { x+3 }{ 2 } $$.

A
$$x=-\displaystyle\frac { 31 }{ 5 } $$

B
$$x=-\displaystyle\frac { 11 }{ 5 }$$

C
$$x= \displaystyle\frac { 31 }{ 9 }$$

D
$$x=-\displaystyle\frac { 26 }{ 5 } $$

Solution

Given, $$\displaystyle\frac { x-5 }{ 7 } =\displaystyle\frac { x+3 }{ 2 } $$
$$\Rightarrow \displaystyle 2(x-5)=7(x+3)$$ .....(By cross multiplication of denominators)
$$\Rightarrow2x-10=7x+21$$ ...(By Distribution Law).

Transposing $$x$$ terms to one side, we get,
$$\Rightarrow 7x-2x=-10-21$$
$$\Rightarrow 5x=-31$$
$$\Rightarrow x=\cfrac{-31}{5}$$.

Hence, option $$A$$ is correct.
Question 2
1 / -0

If $$x-4=5$$, then the value of $$x$$ is-

A
$$-1$$

B
$$9$$

C
$$-9$$

D
$$1$$

Solution

$$x-5=4$$ $$\Rightarrow$$ $$x=5+4=9$$
Question 3
1 / -0

Lalit's brother is thrice as old as Lalit. If brother's age is 60 years then Lalit's age is

A
30 yrs

B
10 yrs

C
20 yrs

D
60 yrs

Solution

Let Lalit brothers age be 3x and Lalit's age be x.
3x = 60
x = $$\displaystyle{\frac{60}{3}}$$ = 20
Question 4
1 / -0

Find $$x$$, if $$12-(9+3x)=18x$$.

A
$$\dfrac{-1}{7}$$

B
$$\dfrac{7}{5}$$

C
$$\dfrac{1}{7}$$

D
$$-7$$

Solution

Given, $$\displaystyle 12-(9+3x)=18x$$.

$$\Longrightarrow \displaystyle 12-9-3x=18x$$ ...[By Distribution Law]

$$\Longrightarrow\displaystyle -3x+3=18x$$ ...[On simplifying].

Transposing $$x$$ terms to one side, we get,

$$\Longrightarrow\displaystyle 18x+3x=3$$

$$\Longrightarrow 21x=3$$

$$\Longrightarrow x=\dfrac{3}{21}$$

$$\Longrightarrow x=\dfrac{1}{7}$$.

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

Linear equation in one variable has

A
Only constant term.

B
Only one variable with power $$1$$.

C
Only one term with a variable.

D
Only one variable with any power.

Solution

$${\textbf{Step-1: Use definition of linear equation in one variable }}$$
$$\text{Linear equation is in the form ax+b=0 where x is variable and a and b are constants}$$
$${\text{Example, 5x-10=5 has only one variable.}}$$
$${\textbf{Hence, answer is an equation one variable raised to the power 1.}}$$
Question 6
1 / -0

Solve the equation: $$\dfrac{7x - 3}{3x}=2$$

A
$$x=3$$

B
$$x=2$$

C
$$x=1$$

D
$$x=-1$$

Solution

$$\dfrac{7x - 3}{3x}=2$$
$$7x - 3 = 6x$$
On transposing $$6x$$ to the L.H.S and $$3$$ to the R.H.S we obtain
$$7x - 6x = 3$$
$$x = 3$$
Question 7
1 / -0

Find the value of $$ p$$ in the linear equation: $$4p + 2 = 6p + 10$$

A
$$p=-4$$

B
$$p=-3$$

C
$$p=-2$$

D
$$p=-1$$

Solution

$$4p + 2 = 6p + 10$$

$$6p - 4p =2-10$$

$$2p = -8$$

$$p = -4$$
Question 8
1 / -0

If $$1$$ is subtracted from a number it becomes $$\dfrac{1}{8}$$. Find the original number.

A
$$\dfrac{8}{9}$$

B
$$\dfrac{-9}{8}$$

C
$$\dfrac{9}{8}$$

D
None of the above.

Solution

Let original number be $$x$$.
$$\displaystyle \therefore x-1=\dfrac { 1 }{ 8 }$$

$$\therefore x=1+\dfrac { 1 }{ 8 } $$

$$\therefore x=\dfrac { 9 }{ 8 } $$
Question 9
1 / -0

Reduce the following linear equation: $$2x + 5 = 3$$

A
$$x=1$$

B
$$x=-1$$

C
$$x=0$$

D
$$x=2$$

Solution

Given, $$2x + 5 = 3$$

$$2x = 3 - 5$$
$$2x = -2$$
$$x = -1$$
Question 10
1 / -0

$$\dfrac{3}{5}$$th of a number subtracted from $$\dfrac{3}{4}$$th of that number gives $$18$$. Find the number.

A
$$110$$

B
$$100$$

C
$$120$$

D
None of the above.

Solution

Let the required number be $$x$$.

According to the question: $$\displaystyle \frac { 3 }{ 4 } x-\frac { 3 }{ 5 } x=18$$

$$\Longrightarrow\displaystyle \frac { 3x\times 5-3x\times 4 }{ 20 } =18$$

$$\Longrightarrow\displaystyle 15x-12x=18\times 20$$

$$\Longrightarrow\displaystyle 3x=18\times 20$$

$$\Longrightarrow\displaystyle x=6\times 20$$

$$\therefore x=120$$

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Linear Equations in One Variable Test - 21

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Linear Equations in One Variable Test - 21

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Question 1

$$x=-\displaystyle\frac { 31 }{ 5 } $$

$$x=-\displaystyle\frac { 11 }{ 5 }$$

$$x= \displaystyle\frac { 31 }{ 9 }$$

$$x=-\displaystyle\frac { 26 }{ 5 } $$

Solution

Question 2

$$-1$$

$$9$$

$$-9$$

$$1$$

Solution

Question 3

30 yrs

10 yrs

20 yrs

60 yrs

Solution

Question 4

$$\dfrac{-1}{7}$$

$$\dfrac{7}{5}$$

$$\dfrac{1}{7}$$

$$-7$$

Solution

Question 5

Only constant term.

Only one variable with power $$1$$.

Only one term with a variable.

Only one variable with any power.

Solution

Question 6

$$x=3$$

$$x=2$$

$$x=1$$

$$x=-1$$

Solution

Question 7

$$p=-4$$

$$p=-3$$

$$p=-2$$

$$p=-1$$

Solution

Question 8

$$\dfrac{8}{9}$$

$$\dfrac{-9}{8}$$

$$\dfrac{9}{8}$$

None of the above.

Solution

Question 9

$$x=1$$

$$x=-1$$

$$x=0$$

$$x=2$$

Solution

Question 10

$$110$$

$$100$$

$$120$$

None of the above.

Solution

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