# Ex.4.2 Q3 Simple-Equations Solution - NCERT Maths Class 7

## Question

Give the steps you will use to separate the variable and then solve the equation:

(a) \(\begin{align}3n-2 = 46\end{align}\)

(b) \(\begin{align}5m + 7 = 17\end{align}\)

(c) \(\begin{align}\frac{{20p}}{3} = 40\end{align}\)

(d) \(\begin{align}\frac{{3p}}{{10}} = 6\end{align}\)

## Text Solution

**What is Known?**

Equations

**What is unknown?**

The first step we use to separate the variable in order to solve the equations.

**Reasoning:**

First try to reduce the equation by adding, subtracting, multiplying or dividing both sides of the equation by the same number to get the value of variable.

**Steps:**

(a) \(3n-2 = 46\)

Adding \(2\) to both sides of the equation, we get

\[\begin{align}3n-2 + 2 &= 46 + 2\\3n &= 48\end{align}\]

Dividing both the sides by \(3\) we get,

\[\begin{align}\frac{{3n}}{3} = \frac{{48}}{3}\\n = 16\end{align}\]

(b) \(5m + 7 = 17\)

Subtracting \(7\) from both sides of the equation, we get

\[\begin{align}5m + 7 - 7 &= 17 - 7\\5m& = 10\end{align}\]

Dividing both the sides by \(5\) we get,

\[\begin{align}\frac{{5m}}{5} &= \frac{{10}}{5}\\m &= 2\end{align}\]

(c) \(\begin{align}\frac{{20p}}{3} = 40\end{align}\)

Multiplying both the sides by \(3\) we get,

\[\begin{align}\frac{{20p}}{3} \times 3 &= 40 \times 3\\20p &= 120\end{align}\]

Dividing both the sides by \(20\) we get,

\[\begin{align}\frac{{20p}}{{20}} &= \frac{{120}}{{20}}\\p &= 6\end{align}\]

(d) \(\begin{align}\frac{{3p}}{{10}} = 6\end{align}\)

Multiplying both the sides by \(10\) we get,

\[\begin{align}\frac{{3p}}{{10}} \times 10 &= 6 \times 10\\3p &= 60\end{align}\]

Dividing both the sides by \(20\) we get,

\[\begin{align}\frac{{3p}}{3} &= \frac{{60}}{3}\\p &= 20\end{align}\]