# Ex.4.2 Q1 Simple-Equations Solution - NCERT Maths Class 7

## Question

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

(a) \( x \,– 1 = 0\)

(b) \(x + 1 = 0\)

(c) \(x\, – 1 = 5\)

(d) \(x + 6 = 2\)

(e) \(y \,– 4 = \,– 7\)

(f) \(y\, – 4 = 4 \)

(g) \(y + 4 = 4\)

(h) \(y + 4 = \,– 4\)

## Text Solution

**What is Known?**

Equations.

**What is unknown?**

The first step which should be used to separate the variable in order to solve the equation.

**Reasoning:**

First try to reduce the equation by adding or subtracting by the same number and get the value of variable.

**Steps:**

(a) \( x \,– 1 = 0\)

Adding one to both sides of the equation we get,

\[\begin{align}x-1 + 1 &= 0 + 1\\x &= 1\end{align}\]

(b) \(x + 1 = 0\)

Subtracting one from both sides of the equation we get,

\[\begin{align}x + 1 -1 &= 0 -1\\x &= - 1\end{align}\]

(c) \(x \,– 1 = 5\)

Adding one to both sides of the equation we get,

\[\begin{align}x-1 + 1&= 5 + 1\\x &= 6\end{align}\]

(d) \(x + 6 = 2\)

Subtracting \(6\) from both sides of the equation we get,

\[\begin{align}x + 6 -6 &= 2 -6\\x &= -4\end{align}\]

(e) \(y \,– 4 = – 7\)

Adding \(4\) to both sides of the equation we get,

\[\begin{align}y-4 + 4 &= -7 + 4\\y &= -3\end{align}\]

(f) \(y \,– 4 = 4 \)

Adding \(4\) to both sides of the equation we get,

\[\begin{align}y-4 + 4 &= 4 + 4\\y &= 8\end{align}\]

(g) \(y + 4 = 4\)

Subtracting \(4\) from both sides of the equation we get,

\[\begin{align}y + 4 -4 &= 4 -4\\y &= 0\end{align}\]

(h) \(y + 4 = – 4\)

Subtracting \(4\) from both sides of the equation we get,

\[\begin{align}y + 4 -4&= -4 -4\\y &=-8\end{align}\]