Ex.12.3 Q7 Algebraic Expressions Solution - NCERT Maths Class 7

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Question

 Simplify these expressions and find their values if \(x = 3\), \(a = \,– 1\), \(b =\, – 2\).

(i) \(3x - 5 - x + 9 \)

(ii) \(2 - 8x + 4x + 4\)

(iii) \(3a + 5 - 8a + 1 \)

(iv) \(10 - 3b - 4 - 5b\)

(v) \(2a - 2b - 4 - 5 + a\)

Text Solution

What is Known?

Value of \(x\), \(a\) and \(b\)

What is unknown?

Value of the given expressions.

Reasoning:

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

Steps:

Value of \(x\) is given as \(3\), \(a\) as \(-1\) and \(b\) is \(-2\)

(i) \(3x - 5 - x + 9 \)

\[\begin{align}& = 2x + 4\\&\text{ Now putting value of }x = 3\\& = \left( {2 \times 3} \right) + 4\\& = 6 + 4\\{\text{ Ans }} & = 10\end{align}\]

(ii) \(2 - 8x + 4x + 4\)

\[\begin{align}& = - 4x + 6\\&\text{ Now putting value of x = 3}\\& = \left( { - 4 \times 3} \right) + 6\\& = - 12 + 6\\{\text{ Ans }} & = - 6\end{align}\]

(iii) \(3a + 5 - 8a + 1 \)

\[\begin{align}& = - 5a + 6\\&\text{ Now putting value of a = - 1}\\& = \left( { - 5\,\, \times - 1} \right) + 6\\
 & = 5 + 6\\{\text{ Ans }} & = 11\end{align}\]

(iv) \(10 - 3b - 4 - 5b\)

\[\begin{align}& = - 8b + 6\\&\text{ Now putting value of b = - 2}\\& = ( - 8 \times - 2) + 6\\& = 16 + 6\\{\text{ Ans }} & = 22\end{align}\]

(v) \(2a - 2b - 4 - 5 + a\)

\[\begin{align}& = 3a - 2b - 9\\&\text{Now putting value of }a = - 1\,\text{and}\,{\rm{ }}b = - 2\\&\left( {3 \times - 1} \right) - \left( {2 \times - 2} \right) - 9\\& = - 3 - ( - 4) - 9\\ & = - 3 + 4 - 9\\{\text{Ans}} & = - 8\,\end{align}\]