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

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## Question

Give first the step 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}

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