Solving Equations with Variables on Both Sides

Q. Question 10
$3m=5m-\frac{8}{5}$

Q.

If $2a=3b=4c$, then $a:b:c$?

Q.

Two years ago, father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Find their presents ages.

Q.

Solve :

$\frac{5x-4}{6}=4x+1-\frac{3x+10}{2}$

Q. The present age of Sahil’s mother is three times the present age of Sahil. After 5 years their ages will add to 66 years. Find their present ages.
[2 marks]

Q. Solve the following equation and check your result:
$\frac{2x}{3}+1=\frac{7x}{15}+3$

Q.

The sum of two numbers is 45 and their ratio is 7 : 8. Find the numbers.

Q.

The ages of Sonu and Monu are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

Q.

Question 51

Solve the following:

$\frac{2x-3}{4x+5}=\frac{1}{3}$

Q.

If $\frac{4x+8}{5x+8}=\frac{5}{6}$, then x = ?

(a) 4

(b) 6

(c) 8

(d) 12

Q.

Question 63

Solve the following:

$\frac{1}{2}(x+1)+\frac{1}{3}(x-1)=\frac{5}{12}(x-2)$

Q.

Solve the following equations and verify your answer :

$\frac{5x-7}{3x}=2$

Q.

A number whose fifth part increased by 5 is equal to its fourth part diminished by 5. Find the number.

Q.

Solve :

$\frac{3x}{5x+2}=-4$

Q.

Solve :

9x + 5 = 4 (x - 2) + 8

Q.

Solve for x:
(x+5)/6−(x+1)/9=(x+3)/4

(a) −2/7

(b) −1/7

(c) −5/7

(d) 7

Q.

If $8x–3=25+17x$, then $x$ is:

1. a fraction

2. an integer

3. a rational number

4. cannot be solved

Q.

Sum of two natural numbers is $8$ and the difference of their reciprocals is $\frac{2}{15}$. Find the numbers.

Q.

If $\frac{x+1}{2x+3}=\frac{3}{8}$, then x = ?

(a) $\frac{1}{4}$

(b) $\frac{1}{3}$

(c) $\frac{1}{6}$

(d) $\frac{1}{2}$

Q.

Solve :

$\frac{6y-5}{2y}=\frac{7}{9}$

Q.

Solve :

$\frac{4x+7}{9-3x}=\frac{1}{4}$

Q.

The denominator of a fraction is $1$ less than twice its numerator. If $1$ is added to numerator and denominator respectively, the ratio of numerator to denominator is $3:5$ Find the fraction.

Q.

Solve :

$5x-\frac{1}{3}(x+1)=6(x+\frac{1}{30})$

Q.

Solve :

5x + 7 = 2x - 8

Q.

Solve :

$\frac{3(y-5)}{4}-4y=3-\frac{(y-3)}{2}$

Q. Solve for m: $m-\frac{m-1}{2}=1-\frac{m-2}{3}$

Q.

Solve each of the following equations and also verify your solution :

$\frac{7y+2}{5}=\frac{6y-5}{11}$

Q. Solve $2x+5=3(x+2)$ for $x$.

1. -1
2. 3
3. 1
4. -2

Q.

Question 56

Solve the following:

$\frac{x}{5}=\frac{x-1}{6}$

Q.

Solve the following equations and verify your answer :

$\frac{1-9y}{19-3y}=\frac{5}{8}$