Simple Equations Test

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Simple Equations Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

$$12$$ times a number is $$4$$ less than the $$5$$ times the number. Write an equation representing the statement given.

A
$$12x -4 = 5x$$

B
$$12x+4 = 5x$$

C
$$12+ 4x= 5$$

D
$$12 -4x= 5$$

Solution

Let the number be $$x$$
$$\Rightarrow 12\times x=5\times x-4 $$
$$\Rightarrow 12x+4=5x$$
Question 2
1 / -0

The value of x in the equation $$5x - 35 = 0$$ is:

A
$$2$$

B
$$7$$

C
$$8$$

D
$$11$$

Solution

Given, $$5x-35=0$$

Transpose $$35$$ to R.H.S.,
$$5x=35$$

Divide throughout by $$5$$
$$\dfrac {5x}{5}=\dfrac {35}{5}$$

$$\Rightarrow x=7$$
Question 3
1 / -0

Three times the number is $$300$$. Convert this statement in mathematical form.

A
$$3x=100$$

B
$$3+x=300$$

C
$$3 =300+x$$

D
$$3x=300$$

Solution

$$3$$ times the number is $$300.$$
$$\Rightarrow$$ Let the number $$=x$$
$$\Rightarrow 3$$ times the number $$=3x$$
$$\Rightarrow$$ This is equal to $$3x=300.$$
Hence, the answer is $$3x=300.$$
Question 4
1 / -0

The substraction of 3 from 2x is represent as

A
2x-3

B
3-2x

C
2x+3

D
$$\frac{2x}{3}$$

Solution

Subtraction $$3$$ from $$2x=2x-3$$
Question 5
1 / -0

Is this an equation $$21=z+11$$

A
$$Yes$$

B
$$NA$$

C
$$No$$

D
$$15$$

Solution

$$21=z+11$$ is a equation
Question 6
1 / -0

If $$20 = 6 + 2x$$, then the value of $$x$$ is:

A
$$6$$

B
$$9$$

C
$$8$$

D
$$7$$

Solution

Given, $$20=6+2x$$
Subtract $$6$$ on both the sides,
$$20-6=6+2x-6$$
$$14=2x$$
Divide $$2$$ on both the sides, we get
$$\dfrac {14}{2} = \dfrac { 2x}{ 2} $$
$$\Rightarrow x=7$$
Hence the answer is option $$D$$.
Question 7
1 / -0

If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:

A
changes

B
remains the same

C
changes in case of multiplication only

D
changes in case of division only

Solution

Let us take an equation $$x+2y=5$$ .....(1)
Put $$x=1$$ in eqn (1)
$$ \Rightarrow y=2$$
So,$$x=1,y=2$$ is a solution of the equation
Multiplying both sides of equation 1() by $$3$$, we get
$$3x+6y=15$$
Put $$x=1, y=2$$ in LHS
LHS $$=3\times 1+6\times 2=15=$$ RHS
Hence, on multiplying an equation by a non-zero number , the solution remains same.

Let us divide both sides of equation (1) by $$2$$
$$\Rightarrow \displaystyle \frac{x}{2}+y=\frac{5}{2}$$
Put $$x=1,y=2$$ in above equation
LHS $$=\displaystyle \frac{1}{2}+2=\frac{5}{2}=$$ RHS
Hence, on dividing or multiplying an equation by a non-zero number, the solution remains the same.
Question 8
1 / -0

If the mean of observations $$x, x + 2, x + 4, x + 6$$ and $$x + 8$$ is $$11$$, find the value of $$x$$:

A
$$8$$

B
$$5$$

C
$$6$$

D
$$7$$

Solution

Mean of observations $$x, x + 2, x + 4, x + 6, x + 8$$ is $$11$$
Mean $$= \cfrac{\text{Sum}}{\text{Number of observation}}$$
Mean $$= \cfrac{x + x +2 + x + 4 +x + 6 + x + 8}{5} = 11$$
$$\cfrac{5x + 20}{5} = 11$$
$$5x + 20 = 55$$
$$5x = 55 - 20$$
$$5x = 35$$
$$x = 7$$
Hence the answer is option $$D$$
Question 9
1 / -0

$$x = 5, y = 2$$ is a solution of the linear equation

A
$$x + 2 y = 7$$

B
$$5x + 2y = 7$$

C
$$x + y = 7$$

D
$$5 x + y = 7$$

Solution

$$\textbf{Step 1: Check which of the equation passes through (5,2).}$$

$$\text{The solution should satisfy the appropriate equation.}$$
$$\text{So, let us investigate each option by substituting }x=5$$ & $$y=2$$

$$(A)$$ $$x+2y=7$$.
$$\text{L.H.S. }=5+2\times 2=9\neq$$ $$\text{R.H.S.}$$
$$ \therefore$$ $$\text{It is not the appropriate equation.}$$

$$(B)$$ $$5x+2y=7$$
$$\text{L.H.S. }=5\times 5+2\times 2=29\neq$$ $$\text{R.H.S.}$$
$$\therefore $$ $$\text{It is not the appropriate equation.}$$

$$(C)$$ $$x+y=7$$
$$\text{L.H.S. }=5+2=7=$$ $$\text{R.H.S}$$
$$\therefore$$ $$\text{It is the appropriate equation.}$$

$$(D)$$ $$ 5x+y=7$$
$$\text{L.H.S. }=5\times 5+2=27\neq$$ $$\text{R.H.S.}$$
$$\therefore $$ $$\text{It is not the appropriate equation.}$$

$$\textbf{Hence, option C is correct.}$$
Question 10
1 / -0

Find the value of $$p $$ in the equation
$$\dfrac{p}{9}-8=17$$

A
$$225$$

B
$$-225$$

C
$$\dfrac{225}{9}$$

D
$$\dfrac{9}{225}$$

Solution

$$\frac { p }{ 9 } -8=17$$

$$\Longrightarrow\displaystyle \frac { p }{ 9 } =17+8$$

$$\Longrightarrow \dfrac { p }{ 9 } =25$$
Now, multiplying both sides by $$9$$ we get,
$$\Longrightarrow\displaystyle \frac { p }{ q } \times 9=25\times 9=225$$

$$\Longrightarrow\displaystyle p=225$$

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Simple Equations Test - 17

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Simple Equations Test - 17

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SHARING IS CARING

Question 1

$$12x -4 = 5x$$

$$12x+4 = 5x$$

$$12+ 4x= 5$$

$$12 -4x= 5$$

Solution

Question 2

$$2$$

$$7$$

$$8$$

$$11$$

Solution

Question 3

$$3x=100$$

$$3+x=300$$

$$3 =300+x$$

$$3x=300$$

Solution

Question 4

2x-3

3-2x

2x+3

$$\frac{2x}{3}$$

Solution

Question 5

$$Yes$$

$$NA$$

$$No$$

$$15$$

Solution

Question 6

$$6$$

$$9$$

$$8$$

$$7$$

Solution

Question 7

changes

remains the same

changes in case of multiplication only

changes in case of division only

Solution

Question 8

$$8$$

$$5$$

$$6$$

$$7$$

Solution

Question 9

$$x + 2 y = 7$$

$$5x + 2y = 7$$

$$x + y = 7$$

$$5 x + y = 7$$

Solution

Question 10

$$225$$

$$-225$$

$$\dfrac{225}{9}$$

$$\dfrac{9}{225}$$

Solution

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