Introduction to Algebra

Look at the following pattern and fill up the missing boxes.

State the rule which connects the quantities in the different columns. Find the generalised statement for $n$ in each case.

There are $4$ girls in a class. If $y$ more girls join the class, then the total number of girls in the class will be _____.

The solution of $3x + 4 = 8-x$ is $x =$_____.

$5$ times $s$ subtracted from $8$ times $t$ is _____.

A term of the expression having no literal factor is called a constant term. 

A spends $₹x$ and earns $₹y$ everyday. If he spends less than what he earns, then in a week he saves $₹7\left(x-y\right)$. 

If a number $n$ is multiplied by $3$ and then $5$ is subtracted from the result, I get $76$. The equation to find the number is $5-3n=76$. 

The value of $x$ which satisfies the equation $3x-5=\frac{5}{2} x-1$ is $8$.

The present age of a brother is $5$ years more than that his sister. If the sum of their present ages is $21$ years, the present age of the sister is 

If $12x-8=-152$, the value of $x$ is

In the given Fig., $ABCD$ is a rectangle. If its perimeter is $84 \mathrm{cm}$, the value of $x$ is

In the given Fig., degree measures of the angles of $△ABC$ are given in $x$. The value of $x$ is 

If $5$ less than the four-fifths of a number is $47$, then the number is 

On solving an equation $2x-\frac{1}{2}=-5$, we get 

The solution of $5x-23=-8$ is 

An equation is solved as follows:

$x-6=4 \text{or} x=4+6 \text{or} x = 10$

This method of solution is called 

Which of the following is not an equation? 

The marks obtained by a student in a mathematics test is $8$ more than two-thirds of $x$. If $x = 60$, then marks obtained by the student is

For the sequence $-1, 2, 5, 8, 11, ....$, find the general rule, the $n^{\mathrm{th}}$ term and the ${100}^{\mathrm{th}}$ term.

The polynomial $\left(2xy-9\right)$ is