Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

When a number is divided by $$25$$, the result is $$-25$$. The number is:

A
$$625$$

B
$$-625$$

C
$$15625$$

D
$$3125$$

Solution

Let the required number be $$ x$$.

According to the question,
$$\displaystyle \dfrac { x }{ 25 } =-25$$

$$\displaystyle x=-25\times 25$$ .......Multiply both sides by $$25$$

$$\displaystyle x=-625$$
Question 2
1 / -0

Find $$v$$, if $$\displaystyle v+11=77-9v$$.

A
$$\dfrac{33}{5}$$

B
$$\dfrac{5}{33}$$

C
$$-\dfrac{5}{33}$$

D
$$\dfrac{15}{33}$$

Solution

Given, $$\displaystyle v+11=77-9v$$.

Transposing $$v$$ terms to one side, we get,
$$\Longrightarrow\displaystyle v+9v=77-11 $$

$$\Longrightarrow 10v=66$$

$$\Longrightarrow\displaystyle v=\dfrac{66}{10}$$

$$\therefore v=\dfrac{33}{5}$$.

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

If $$\displaystyle 4(3-n)=3n$$, then find the value of $$n$$.

A
$$\dfrac{7}{12}$$

B
$$-\dfrac{12}{7}$$

C
$$\dfrac{12}{7}$$

D
$$-\dfrac{7}{12}$$

Solution

Given, $$\displaystyle 4(3-n)=3n$$
$$\Longrightarrow\displaystyle 12-4n=3n$$ ...[By Distribution Law].

Transposing $$n$$ terms to one side, we get,
$$\Longrightarrow\displaystyle -4n-3n=-12$$
$$\Longrightarrow\displaystyle -7n=-12$$
$$\Longrightarrow\displaystyle n=\dfrac{12}{7}$$.

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

The sum of four consecutive even integers is $$92$$. Find the largest number.

A
$$20$$

B
$$22$$

C
$$24$$

D
$$26$$

Solution

Let four consecutive even numbers be:
$$\displaystyle x,x+2,x+4,x+6$$

According to the question,
$$\displaystyle x+x+2+x+4+x+6=92$$

$$\Longrightarrow\displaystyle 4x+12=92$$

$$\displaystyle x=\dfrac{80}{4}=20$$

$$\therefore$$ the largest number among them is $$x+6$$ = $$20+6$$ = $$26$$
Question 5
1 / -0

$$10$$ is subtracted from the product of $$x$$ and $$9$$, the result is $$80$$. The number is

A
$$20$$

B
$$10$$

C
$$1$$

D
$$9$$

Solution

According to the question,
$$\displaystyle 9x-10=80$$
$$\Longrightarrow\displaystyle 9x=80+10$$ (on transposing)
$$\Longrightarrow\displaystyle 9x=90$$
$$\Longrightarrow\displaystyle x=\frac { 90 }{ 9 } =10$$
Question 6
1 / -0

Calculate the value of $$x$$, when $$2x+3=3x-4$$.

A
$$-7$$

B
$$-\cfrac{1}{5}$$

C
$$1$$

D
$$\cfrac{1}{5}$$

E
$$7$$

Solution

Given, $$\ 2x+3=3x-4$$.

Transposing $$x$$ terms to one side, we get,
$$\Rightarrow 2x-3x=-4-3$$

$$\Rightarrow -x=-7$$

$$\Rightarrow x=7$$.

Hence, option $$E$$ is correct.
Question 7
1 / -0

Solve the equation: $$\dfrac{x+2}{2x}=1$$

A
$$x=2$$

B
$$x=3$$

C
$$x=4$$

D
$$x=5$$

Solution

Given, $$\dfrac{x+2}{2x}=1$$
Multiplying both sides by $$2x$$, we obtain
$$x + 2 = 2x$$
$$2x - x = 2$$
$$x = 2$$
Question 8
1 / -0

If $$x + 1 = 23$$, calculate the value of $$3x + 3$$.

A
$$22$$

B
$$46$$

C
$$66$$

D
$$69$$

Solution

Given that, $$x+1=23$$
To find out: The value of $$3x+3$$

$$x+1=23$$
$$\therefore \ x=23-1=22$$

Hence, $$3x+3 =3\left( 22 \right) +3\quad \quad [\because \ x=22]$$
$$\Rightarrow 66+3=69$$

Hence, if $$x+1=23$$, then the value of $$3x+3$$ is $$69$$.
Question 9
1 / -0

Find the value of $$x$$ which satisfies $$\displaystyle 5x+3=10x-17$$.

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

E
$$5$$

Solution

Given, $$5x+3=10x-17$$.

Transposing $$x$$ terms to one side, we get,
$$\Rightarrow 5x-10x=-17-3$$

$$\Rightarrow -5x=-20$$

$$\Rightarrow x=\dfrac{-20}{-5}$$

$$\Rightarrow x=4$$.

Hence, option $$D$$ is correct.
Question 10
1 / -0

Solve for $$x$$:
$$\dfrac {7}{3x + 4} = \dfrac {7}{6x - 2}$$

A
$$-2$$

B
$$-1$$

C
$$0$$

D
$$2$$

Solution

Given,
$$\dfrac { 7 }{ 3x+4 } =\dfrac { 7 }{ 6x-2 } $$
$$\Rightarrow 42x-14=21x+28$$
$$\Rightarrow 42x-21x=28+14$$
$$\Rightarrow 21x=42$$
$$\Rightarrow x=2$$

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Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 22

Result

Linear Equations in One Variable Test - 22

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SHARING IS CARING

Question 1

$$625$$

$$-625$$

$$15625$$

$$3125$$

Solution

Question 2

$$\dfrac{33}{5}$$

$$\dfrac{5}{33}$$

$$-\dfrac{5}{33}$$

$$\dfrac{15}{33}$$

Solution

Question 3

$$\dfrac{7}{12}$$

$$-\dfrac{12}{7}$$

$$\dfrac{12}{7}$$

$$-\dfrac{7}{12}$$

Solution

Question 4

$$20$$

$$22$$

$$24$$

$$26$$

Solution

Question 5

$$20$$

$$10$$

$$1$$

$$9$$

Solution

Question 6

$$-7$$

$$-\cfrac{1}{5}$$

$$1$$

$$\cfrac{1}{5}$$

$$7$$

Solution

Question 7

$$x=2$$

$$x=3$$

$$x=4$$

$$x=5$$

Solution

Question 8

$$22$$

$$46$$

$$66$$

$$69$$

Solution

Question 9

$$1$$

$$2$$

$$3$$

$$4$$

$$5$$

Solution

Question 10

$$-2$$

$$-1$$

$$0$$

$$2$$

Solution

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