Solution of Linear Equation in One Variable

Write the new equation formed by doing the given operation:

Write whether the given statement is true or false:

The value of $x$ in equation $\frac{9x}{x+5}=4$ is $4$.

Write the new equation formed by doing the given operation:

Solve the rational equation given in one variable:

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

Find the equation we get on subtracting $4x$ from both the sides of equation $17x-8=22$.

Find a number whose fifth part increased by $30$ is equal to its fourth part increased by $23$.

A triangle has two equal sides and each $4 \mathrm{m}$ less than three times the third side, and its perimeter is $55 \mathrm{m}$. If the third side of the triangle is $k \mathrm{m}$, then find the value $k$.

Solve the following equation: $5x-12=2x-6$

Twice a number is as much greater than $30$ as the three times of the number less than $60$. The number is

If two angles are complementary and one angle is $10°$ greater than the other, and the smaller angle of the two is $x°$ then find $x$.

When$9$ is added to two times a number, we get $67$. The number is

What should be added to $\frac{-7}{3}$ to get $\frac{3}{7}$?

Three numbers are in ratio $3:4:5$, the sum of their cubes is $729000.$ Find the sum of these three numbers.

If $\mathrm{x}$ is a rational number and $\frac{(x+1{)}^3-(x-1{)}^3}{(x+1{)}^2-(x-1{)}^2}=2$ then the sum of numerator and denominator of $\mathrm{x}$ is_____.

Find the solution of the following equation- (Write the answer as an improper fraction)

$7-3x=18$

What should be added to five-seventh of rational number $\frac{-3}{5}$, so that it becomes $\frac{3}{7}$?

A rational number $x$ is such that when multiplied by $\frac{3}{4}$ and added to $5$, it becomes $\frac{1}{2}$. Find the rational number.

Find the value of $a$ in decimal form up to two decimal places: $0.25(8a-0.5)=7.5$

If $x$ should be subtracted from thrice the rational number $\frac{-13}{4}$ to get $\frac{5}{8}$, find the value of $8x$.

Find the value of $x$ in fractional form: $\frac{13}{5}-5x=13$