# EXERCISE 2.1

Question 1 :

Solve : x-2=7

sol : x-2=7

On transposing 2 to R.H.S , we obtain

x=7+2=9

Question 2 :

Solve : y+3=10

sol :

y+3=10

On transposing 3 to R.H.S , we obtain

y= 10-3 = 7

Question 3 :

Solve : 6 =z+2

sol :

6 = z+2

On transposing 2 to L.H.S , we obtain

6-2 = z

z=4

Question 4 :

Solve : ​$$\dfrac{3}{7}+x=\dfrac{17}{7}$$

sol :

$$\dfrac{3}{7}+x=\dfrac{17}{7}$$

On transposing ​$$\dfrac{3}{7}$$​ to R.H.S , we obtain

\begin{align*}x&=\dfrac{17}{7}-\dfrac{3}{7}\\&=\dfrac{14}{7}\\&=2\end{align*}

Question 5 :

Solve : 6x=12

sol :

6x=12

Dividing both side by 6 , we obtain

$$\dfrac{6x}{6}=\dfrac{12}{6}$$

Question 6 :

Solve : ​$$\dfrac{t}{5}=10$$

sol :

$$\dfrac{t}{5}=10$$

Multiplying both side by 5, we obtain

$$\dfrac{t}{5}\times5=10\times5$$

t=50

Question 7 :

Solve : ​$$\dfrac{2x}{3}=18$$

sol :

$$\dfrac{2x}{3}=18$$

Multiplying both side by ​$$\dfrac{3}{2}$$​ , we obtain

$$\dfrac{2x}{3}\times\dfrac{3}{2}=18\times\dfrac{3}{2}$$

x=27

Question 8 :

Solve : ​$$1.6=\dfrac{y}{1.5}$$

sol :

$$1.6=\dfrac{y}{1.5}$$

Multiplying both sides by 1.5 , we obtain

$$1.6\times{1.5}=\dfrac{y}{1.5}\times{1.5}$$

2.4=y

Question 9 :

Solve : 7x-9 = 16

sol :

7x-9 = 16

On transposing 9 to R.H.S , we obtain

7x=16+9

7x = 25

Dividing both side by 7 , we obtain

$$\dfrac{7x}{7}=\dfrac{25}{7}$$

$$x=\dfrac{25}{7}$$

Question 10 :

Solve : ​$$14y-8=13$$

sol :

$$14y-8=13$$

On transposing 8 to R.H.S , we obtain

$$14y=13+8\\14y=21$$

Dividing both side by 14 , we obtain

$$\dfrac{14y}{14}=\dfrac{21}{14}$$

$$y=\dfrac{3}{2}$$

Question 11 :

Solve : ​$$17+6p=9$$

sol :

$$17+6p=9$$

On transposing 17 to R.H.S , we obtain

$$6p=9-17$$

$$6p=-8$$

Dividing both side by 6 , we obtain

$$\dfrac{6p}{6}=-\dfrac{8}{6}$$

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

Question 12 :

Solve : ​$$\dfrac{x}{3}+1=\dfrac{7}{15}$$

sol :

$$\dfrac{x}{3}+1=\dfrac{7}{15}$$

On transposing 1 to R.H.S , we obtain

$$\dfrac{x}{3}=\dfrac{7}{15}-1$$

$$\dfrac{x}{3}=\dfrac{7-15}{15}$$

$$\dfrac{x}{3}=-\dfrac{8}{15}$$

Multiplying both sides by 3 , we obtain

$$\dfrac{x}{3}\times{3}=-\dfrac{8}{15}\times{3}$$

$$x=-\dfrac{8}{5}$$