Find the rational number x such that: 5/6x + 3/5x = 5/3x + 1/2 Class 9

Find the rational number x such that: 5/6x + 3/5x = 5/3x + 1/2 Class 9

Question 1.

Find the rational number x such that: $\frac{5}{6}\left(x+\frac{3}{5}\right)=\frac{5}{6} x+\frac{1}{2}$. Class 9

Solution:

Given:

$\frac{5}{6}\left(x+\frac{3}{5}\right)=\frac{5}{6} x+\frac{1}{2}$

L.H.S

$\begin{aligned} & =\frac{5}{6}\left(x+\frac{3}{5}\right) \\ & =\frac{5}{6} \times x+\frac{5}{6} \times \frac{3}{5} \quad \ldots[\text { Distributive Property }] \\ & =\frac{5 x}{6}+\frac{15}{30} \\ & =\frac{5 x}{6}+\frac{1}{2}\end{aligned}$

R.H.S $=\frac{5 x}{6}+\frac{1}{2}$

Thus, L.H.S. = R.H.S. for all values of x.

Since both sides are equal for all values of x, x can be any rational number.

Question 2.

Try and represent $\frac{8}{5}$ and $-\frac{7}{4}$ on a number line. Class 9

Answer:

$\frac{8}{5}=1 \frac{3}{5}$

So, $\frac{8}{5}$ lies between 1 and 2. Divide the interval between 1 and 2 into five equal parts and move three parts to the right of 1.

$-\frac{7}{4}=-1 \frac{3}{4}$

So, $-\frac{7}{4}$ lies between -2 and -1. Divide the interval between -2 and -1 into four equal parts and move three parts to the left of -1.