Ex.12.3 Q3 Algebraic Expressions Solution - NCERT Maths Class 7

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Question

 Find the value of the following expressions, when \(x = \,–1\)

(i) \(2x - 7\)

(ii) \(- x + 2\)

(iii) \({x^2} + 2x + 1\)

(iv) \(2{x^2} - x - 2\)

Text Solution

What is Known?

Value of \(x\)

What is unknown?

Value of the given expressions.

Reasoning:

This is based on concept of putting given value of variable and then performing the arithmetic operation as given in the question.

Steps:

Value of \(x\) is given as \(–1\)

(i) \(2x - 7\)

\[\begin{align}& = 2 \times - 1 - (7)\\& = - 2 - 7\\{\rm{ Ans }} & = - 9\end{align}\]

(ii) \(- x + 2\)

\[\begin{align}& = - \left( { - 1} \right) + 2\\& = 1 + 2\\{\rm{Ans}} & = 3\end{align}\]

(iii) \({x^2} + 2x + 1\)

\[\begin{align}& = {\left( { - 1} \right)^2} + \left( {2 \times - 1} \right) + 1\\& = - 1 \times - 1 + \left( { - 2} \right) + 1\\& = 1 - 2 + 1\\{\rm{ Ans}} & = 0\end{align}\]

(iv) \(2{x^2} - x - 2\)

\[\begin{align}&= 2{{\left( { - 1} \right)}^2} - \left( { - 1} \right) - 2\\&= 2 \times - 1 \times - 1 + 1 - 2\\&= 2 + 1 - 2\\{\rm{ Ans }} &= 1\end{align}\]