Tutorial on How to Solve Equation Step Wise With Examples

Statement where the value of two mathematical expressions is equal is an equation and denoted by the equal sign ‘=’. So generally we face difficulty in solving equations and frequently ask how to solve equations. If you are also strugg;ling with the same then the article will teach you methods to solve the equation. 

Types of equation in mathematics:-

  1. Linear equation
  2. Quadratic equation
  3. Radical equation
  4. Trigonometric equation
  5. Polynomial equation
  6. Exponential equation

Linear equation

These equations are of such type Y=ax+b where ‘a’ and ‘b’ are numbers and ‘x’ cannot be zero.

Quadratic equation

These equations are of such type where one variable out of all contains the exponent of 2. ax²+bx+c=0 is a quadratic equation where x is not equal to zero.

Radical equation

These equations are of such type whose maximum exponent on the variable is ½ and have more than one term. Usually the variables in the radical equation are lying inside a radical symbol in the square root.

Trigonometric equation

These equations are of such types in which variables are affected by trigonometric functions.

Polynomial equation

These equations are of such types in which one takes away the highest exponent limit. In such an equation ‘x’s are all numbers and the equation consists of several terms.

Exponential equation

These equations are of such types that contain variables in place of exponents.

How to solve the equation?

The process of solving equation:

Equation solving having one variables:

Step1: Writing a problem to solve a two step algebraic equation so to visualise the solutions.

Step2: The next step is deciding whether to use addition or subtraction inorder to isolate the variable terms. If one side of the equation is added or subtracted it must be done to another side inorder to maintain the balance.

Step3: On the both sides of equation adding or subtracting the constant on both sides of the equation thus completing the process to isolate the variable term.

Step4: The coefficient of a variable must be eliminated through division or multiplication.

Step5: By dividing the left side of the equation , solve the variables.

How to solve the equation having one variable on each side?

Solving equation having one variable on each sides:

Step1:Writing a problem to solve makes sure the both of variables are the same.

Step2: Constant is moved to the right side of equation.By using addition or subtraction constant is eliminated from the left side of the equations.

Step3: Variables are moved to the left side of the equation by simply additional or subtraction.

Step4: By dividing the both sides of the equation to isolate the variable, solve the variable.

How to solve the two step equation?

However there are others way to solve two step equation:

keeping the variable on the right side of the two step equation can be solved. Answers will be the same as long as variables are isolated.

Multiplying at the end instead of dividing two step equations can be solved. This type of equation is solved by using arithmetic to combine the constants, isolate the variable term and then isolate the variable without the term.

How to solve the equation?

Process of solving linear equation:

Step1: If needed, simplify each side of the equation.

Step2: To move the variable terms on one side and all other terms to the other side use addition or subtraction.

Step3: To remove any values that are in front of the variable use multiplication or division.

Step4: The last step will be checking the answer.

How to solve the equation?

Process of solving quadratic equation:

ax²+bx+c=0 is a quadratic equation where x is not equal to zero.

Step1: All terms should be divided by a (the coefficient of x²)

Step2:Number term i.e (c/a) should be moved to the right side of the equation.

Step3: square on the left side of the equation should be completed and by adding the same value to the right side of the equation balance the equation.

Step4:On both sides of the equation square root is taken.

Step5:Number that remains on the left side of the equation should be subtracted to find x.

How to solve the equation?

Process to solve radical equation:

Equation with one radical:

Step1: Variable and radical is isolated on one side of equations. It is done by combining like terms and adding or subtracting numbers so that the variable and radical stand alone.

Step2: Both sides of the equation are squared inorder to remove radicals. It is done because the equation needs to stay balanced.

Step3: Answer is checked in the original problems to make sures that answer is real. To check an answer simply plug in each answer for ‘x’ in the original equation.

How to solve the equation having multiple radicals?

Equation with multiple radical:

Step1: Inorder to get variables by themselves remove all the radicals at a time and solve the leftover equations.

Step2:One of the variables is isolated under the radicals.

Step3: Squaring both sides of the equation to remove the radical on the left.

Step4: The other square root also needs to be isolated.

Step5: Both sides are squared to simply undo radicals.

Step6: Once all the radicals are gone, solve for ‘x’ using algebra skills.

Step7: Inorder to get the right answer, check all possible solutions.

Conclusion

Inorder to solve equation remember that equation is balance with a sign ‘=’.

If one side of the equation is done something then the same thing must be done to another side in order to keep the equation balanced.

Simply start by simplifying each side of equations and after using addition or subtraction to move every part of the equation that contains the variable on one side and from the constant part isolate the variables and lastly check the solutions by putting back in the original equation. If everything is done correctly the original equation must balance with the solutions. Get the best help for math homework from the experts.