Equations Reducible to the Linear Form

Q.

Solve by factorization method:

$\left(\frac{4}{x}\right)-3=\frac{5}{\left(2x+3\right)},x\ne 0,\frac{-3}{2}$

Q.

The length of a rectangle is twice its breadth. If its perimeter is $72m$ then its length is $24m$

1. False

2. True

Q.

$\frac{3x+5}{4x+2}=\frac{3x+4}{4x+7}.$ Solve this linear equation.

Q.

Solve the given equation:

$\frac{2x+7}{5}-\frac{3x+11}{2}=\frac{2x+8}{3}-5$

Q.

Solve the following systems of equations:

$$\begin{gathered} 152x-378y=-74 \\ -378x+152y=-604 \end{gathered}$$

Q.

Solve :

$\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}$

Q.

Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

1. 17
2. 20
3. 8
4. 3

Q.

Solve The Equation: $3(t–3)=5(2t–1)$

Q.

Solve by using elimination method:

$3x+4y=10and2x-2y=2$

Q.

Question 74

Solve the following:

$\frac{3t-2}{3}+\frac{2t+3}{2}=t+\frac{7}{6}$

Q.

The perimeter of a rectangle is $40m$. Its length is four meters less than five times its breadth. Find the area of the rectangle.

Q.

Solve the following equation: $\frac{9x}{7-6x}=15$.

Q.

If $40$ is subtracted from $60\%$ of a number, the result is $50$. Find the number.

Q.

Question 89

Solve the following:

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Q.

Solve the following equations and verify your answer :

$\frac{2y+5}{y+4}=1$

Q.

Question 68

Solve the following:

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

Q.

Solve the following equations and verify your answer :

$\frac{2x+1}{3x-2}=\frac{5}{9}$

Q.

Solve the following equations and verify your answer :

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

Q.

Solve the following equations and verify your answer :

$\frac{y-(7-8y)}{9y-(3+4y)}=\frac{2}{3}$

Q. What number should be added to $\frac{-7}{8}$ so as to get $\frac{5}{9}$?

1. $\frac{103}{36}$
2. $\frac{103}{72}$
3. $\frac{100}{36}$
4. $\frac{75}{36}$

Q.

Solve the following equations and verify your answer :

$\frac{3x+5}{2x+7}=4$

Q.

Question 73

Solve the following:

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

Q. Solution of the equation 3x + 3 = 15 is ___ .

Q.

The solution for the equation $\frac{x+5}{5x+8}=\frac{11}{38}$ is ___.

Q.

The value of x satisfying the equation $\frac{x+9}{4}+\frac{2x+3}{5}=10$ is 11.

1. False

2. True

Q.

What number must be subtracted from $\frac{1}{4}$ to get $\frac{1}{2}$?

1. 1/2

2. -1/4

3. 1

4. -1

Q. Solve: $\frac{7x}{2}$ - $\frac{5x}{2}$ = $\frac{20x}{3}$ + $10$
(2 marks)

Q.

Rewrite the equation below so that it does not have fractions.

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

Do not use decimals in your answer.

Q.

If $\frac{5}{3x}$ = $\frac{25}{27}$, then x lies between 1 and 2.

1. False

2. True

Q. Question 8
$\frac{2x}{3}+1=\frac{7x}{15}+3$