Tutorial on How to Solve Equation Step Wise With Examples

An equation is a statement in which the values of two mathematical expressions are equal. It is indicated by the equal sign ‘='. As a result, we commonly have problems solving equations and question how to solve equations. If you're having trouble with the same problem, this article will show you how to solve it.

In mathematics, there are various types of equations

Linear equation

These are equations of the form Y=ax+b, where a and b are numbers and x cannot be 0.

Quadratic equation

These equations are of the sort where one of the variables has a two-digit exponent. A quadratic equation in which x is not equal to zero is ax2+bx+c=0.

Radical equation

These equations have more than one term and have a maximum exponent on the variable of 12. In the square root, the variables in the radical equation are usually included within a radical symbol.

Trigonometric equation

These are equations in which the variables are influenced by trigonometric functions.

Polynomial equation

These equations are of the type where the highest exponent limit is removed. The ‘xs' in this equation are all numbers, and the equation is made up of numerous terms.

Exponential equation

These equations are of the type where variables are used instead of exponents.

How do you tackle the problem?

The procedure for solving an equation with only one variable is as follows:

Step 1: To see the solutions, write a problem to solve a two-step algebraic equation.

Step 2: To isolate the variable terms, you must decide whether to employ addition or subtraction. If one side of the equation is added or subtracted, the balance must be maintained on the opposite side.

Step 3: Complete the process of isolating the variable term by adding or removing the constant on both sides of the equation.

Step 4: A variable's coefficient must be removed by division or multiplication.

Step 5: Solve the variables by dividing the left side of the equation.

How do you solve a one-variable problem that has two sides?

Solving an equation with one variable on both sides:

Step 1: When writing a problem to solve, ensure that both variables are the same.

Step 2: The constant is relocated to the right side of the equation. The constant is removed from the left side of the equations by using addition or subtraction.

Step 3: Addition or subtraction are used to transfer variables to the left side of the equation.

Step 4: Solve the variable by dividing both sides of the equation to isolate it.

What is the best way to solve the two-step equation?

However, there are various methods for solving two-step equations, such as maintaining the variable on the right side of the equation. As long as variables are isolated, the results will be the same.

Two step equations can be solved by multiplying at the end rather than dividing. This type of problem is solved by combining the constants, isolating the variable term, and then isolating the variable without the term using arithmetic.

How to solve the equation?

Solving a linear equation:

Step 1: Simplify either side of the equation if necessary.

Step 2: Use addition or subtraction to transfer the variable terms to one side and all other terms to the other.

Step 3: Multiply or divide any values that are in front of the variable to remove them.

Step 4: The final step is to double-check the solution.

The procedure for solving a quadratic equation is as follows:

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

Step 1: Divide all terms by a (the x2 coefficient). Step 2: Move the number term, c/a, to the right side of the equation.

Step 3: Complete the square on the left side of the equation and balance the equation by adding the same number to the right side.

Step 4: The square root is taken on both sides of the equation.

Step 5:To find x, subtract the number that remains on the left side of the equation.

Process to solve radical equation:

Step 1: On one side of the equations, isolate the variable and radical. It's done by grouping like phrases together and adding or subtracting integers until the variable and radical are left alone.

Step 2: To eliminate radicals, both sides of the equation are squared. The reason for this is because the equation must remain balanced.

Step 3: The answer is double-checked against the original problems to ensure that it is correct. Simply plug in each answer for ‘x' in the original equation to check an answer.

Equation with multiple radical:

Step 1: To get variables on their own, eliminate all of the radicals at once and solve the remaining equations.

Step 2: Under the radicals, one of the variables is isolated.

Step 3: Remove the radical on the left by squaring both sides of the equation.

Step 4: Separate the other square root as well.

Step 5: To undo radicals, both sides are squared.

Step6: Using algebra skills, solve for ‘x' once all the radicals have been removed.

Step 7: Check all possible solutions in order to find the correct answer.

Conclusion

Remember that an equation is balanced with a sign ‘=' in order to solve it.

In order to keep the equation balanced, if one side of the equation does something, the other side must do the same.

Simply begin by simplifying each side of the equation, then use addition or subtraction to transfer every component of the equation that contains the variable to one side, isolate the variables from the constant part, and then check the results by re-entering the original equation. The original equation must balance with the solutions if everything is done correctly.