UPSKILL MATH PLUS
Learn Mathematics through our AI based learning portal with the support of our Academic Experts!
Learn moreLinear equations connect the algebraic expression with another algebraic expression or numerical value with the equality sign\((=)\).
Let us recall some basic notations of algebraic expression:
- A variable is a symbol for an unknown value. It is usually denoted in a letter like \(x, y, a, b,\) etc., The word 'variable' means something that can vary, i.e. change. The value of a variable is not fixed. It can take different value.
- Constants are the terms in the algebraic expression that contain only numbers. It is constantly the same(cannot change).Example:\(4\), \(\frac{2}{7}\), \(\sqrt{5}\), \(-0.8\), etc.,
- An algebraic expression is a mathematical expression consist of variables, constants, and the terms in the algebraic expressions are connected by operations.Example:\(2x-2\), \(2x+4\), \(4y\) etc.,
Example:
\(2x + 4\) \(=10\) is the simple linear equation.
Here the expressions \(2x+4\) and \(10\) are connected by equality-sign(\(=\)).
Important!
- In a linear equation, the expression in the left-hand side (LHS) and the expression in the right-hand side (RHS) are equal.
- The value of the variable that satisfies the equation is known as the linear equation solution.
Example:
Check whether the value given in the brackets is a solution to the given linear equation or not: \(7n + 5\) \(= 19\), \((n = 2)\).
A variable value is a solution to the given equation if LHS \(=\) RHS is replaced in the equation by the variable value.
Substitute \(n=2\) in the LHS equation, as:
\(7n +5\) \(=7(2)+5\) \(= 19\).
The LHS value is \(19\), and the RHS value is \(19\).
\(n=2\) is a solution to the linear equation \(7n+5\)\(=19\), since both sides are equal.
Register for free to see more content