Equations Reducible to the Linear Form

Q. Given that a, b and c are three consecutive multiples of 5, where $a,b,c>0$. Choose the correct option(s).

1. a + b + c = 15
2. b = a + 5
3. c = b + 5
4. a = c - 10

Q.

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

1. False

2. True

Q.

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

1. True

2. False

Q.

Solve the equation $\frac{3}{x+1}=\frac{6}{5x-1}$.

1. 3

2. 9

3. 1

4. 2

Q.

The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, then the new number becomes $\frac{3}{2}$. Find the original number.

1. $\frac{8}{11}$

2. $\frac{5}{8}$

3. $\frac{2}{5}$

4. $\frac{7}{10}$

Q.

$\text{Solve for x:}$

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

1. 6

2. 4

3. 5

4. 3

Q.

It is given that "b" has a linear dependency on "a" and "a" has a linear dependency on "c". The equation 3a + 2b + 4c = 5 can be reduced into a linear equation.

1. True

2. False

Q.

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

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Q. $\text{Solve for x:}$

$\frac{x}{a}+\frac{x}{b}=1$

1. $\frac{(a+b)}{b}$
2. $\frac{(a+b)}{ab}$
3. $\frac{b}{a+b}$
4. $\frac{ab}{a+b}$

Q. If $(2x+3{)}^2+(2x-3{)}^2=(8x+6)(x-1)+22$, then the value of '$x$'

1. 4
2. 5
3. - 1
4. 3