Ex.12.3 Q6 Algebraic Expressions Solution - NCERT Maths Class 7

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Question

Simplify the expressions and find the value if \(x\) is equal to \(2\)

(i) \( x + 7 + 4\left( {x - 5} \right)\)

(ii) \(3\left( {x + 2} \right) + 5x - 7\)

(iii) \(6x + 5\left( {x - 2} \right)\)

(iv) \(4\left( {2x - 1} \right) + 3x + 11\)

Text Solution

What is Known?

Value of \(x\)

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. Value of \(x\) is given as \(2\)

Steps:

(i) \( x + 7 + 4\left( {x - 5} \right)\)

\[\begin{align}& =x+7+4x-20 \\ & =5x-13\text{ } \\ & \text{Now putting value of }x=2 \\ 
& 5x-13 \\ & =\left( 5\times 2 \right)-13 \\ & =10-13 \\ \text{ Ans} & =-3 \\ \end{align}\]

(ii) \(3\left( {x + 2} \right) + 5x - 7\)

\[\begin{align}&=3x+6+5x-7  \\&=8x-1\\ &\text{ Now putting value of }x=2  \\&=\left( 8\times 2 \right)-1  \\
&=16-1  \\\text{ Ans} &=15  \\\end{align}\]

(iii) \(6x + 5\left( {x - 2} \right)\)

\[\begin{align}& = 6x + 5x - 10\\& = 11x - 10\\&\text{ Now putting value of }x = 2\\& = \left( {11 \times 2} \right) - 10\\\text{ Ans} & = 12\end{align}\]

(iv) \(4\left( {2x - 1} \right) + 3x + 11\)

\[\begin{align}& = 8x - 4 + 3x + 11\\& = 11x + 7\\&\text{Now putting value of }x = 2\\
& = (11 \times 2) + 7\\ & = 22 + 7\\\text{ Ans} & = 29\end{align}\]