# 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\end{align}

Now putting value of $$x = 3$$

\begin{align}& = \left( {2 \times 3} \right) + 4\\& = 6 + 4\\{\text{ Ans }} & = 10\end{align}

(ii) $$2 - 8x + 4x + 4$$

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

Now putting value of $$x = 3$$

\begin{align}&= \left( { - 4 \times 3} \right) + 6\\& = - 12 + 6\\{\text{ Ans }} & = - 6\end{align}

(iii) $$3a + 5 - 8a + 1$$

\begin{align}= - 5a + 6\end{align}

Now putting value of $$a = - 1$$

\begin{align}&= \left( { - 5\,\, \times - 1} \right) + 6\\ & = 5 + 6\\{\text{ Ans }} & = 11\end{align}

(iv) $$10 - 3b - 4 - 5b$$

\begin{align}& = - 8b + 6\end{align}

Now putting value of  $$b=- 2$$

\begin{align}& = ( - 8 \times - 2) + 6\\& = 16 + 6\\{\text{ Ans }} & = 22\end{align}

(v) $$2a - 2b - 4 - 5 + a$$

\begin{align}& = 3a - 2b - 9\end{align}

Now putting value of $$a = - 1$$ and $$b = - 2$$

\begin{align} &\left( {3 \times - 1} \right) - \left( {2 \times - 2} \right) - 9\\& = - 3 - ( - 4) - 9\\ & = - 3 + 4 - 9\\{\text{Ans}} & = - 8\,\end{align}

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