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Connecting the Dots... - Of Questions and Statements

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An algebraic equation is a condition on a variable. It says that two mathematical expressions are equal. For example, 4x+5=254x + 5 = 25 is an equation.

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A variable is a symbol (like x,y,zx, y, z) that can take different numerical values. Its value is not fixed.

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An equation has an 'equal to' sign (==). The expression to the left is the Left Hand Side (LHS) and the expression to the right is the Right Hand Side (RHS).

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In an equation, the LHS must always be equal to the RHS. If we add, subtract, multiply, or divide both sides by the same non-zero number, the equality still holds.

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Transposition: A term can be moved from one side of the equation to the other by changing its sign. Addition becomes subtraction (++ to −-), and multiplication becomes division (×\times to ÷\div).

📐Formulae

ax+b=cax + b = c

LHS=RHS\text{LHS} = \text{RHS}

If x+a=b, then x=b−a\text{If } x + a = b, \text{ then } x = b - a

If ax=b, then x=ba\text{If } ax = b, \text{ then } x = \frac{b}{a}

💡Examples

Problem 1:

Convert the statement into an equation: 'The sum of three times xx and 1111 is 3232.'

Solution:

3x+11=323x + 11 = 32

Explanation:

Three times xx is written as 3x3x. Adding 1111 to it gives 3x+113x + 11. Since the result is 3232, we equate them.

Problem 2:

Solve the equation: 10y−20=5010y - 20 = 50

Solution:

10y=50+2010y = 50 + 20 10y=7010y = 70 y=7010y = \frac{70}{10} y=7y = 7

Explanation:

First, transpose −20-20 to the RHS, where it becomes +20+20. Then, divide both sides by 1010 to isolate yy.

Problem 3:

Check the result of subtracting 3535 from 100100 using vertical subtraction and use it to solve x+35=100x + 35 = 100.

Solution:

100−3565\begin{array}{r} 100 \\ - 35 \\ \hline 65 \end{array} x=100−35=65x = 100 - 35 = 65

Explanation:

To solve for xx in x+35=100x + 35 = 100, we perform the inverse operation, which is subtraction. The vertical calculation confirms the difference is 6565.