The goal of the process of solving an equation for a variable x is to find the value(s) of the variable for which the equation is true. The solution is written as following:
x=some number or expression
If instead of this you get true statement without a variable, this means that the equation is true regardless of the value of the variable, meaning the solution of the equation is all real numbers or that the equation has infinity solutions.
If instead, you get to a false statement. This means that the equation has no solution. This is because for no values of the variable the equation is true, and the equation is said to have no solutions.
In the end, always substitute your answer in original equation to check your answer.
x=some number or expression
If instead of this you get true statement without a variable, this means that the equation is true regardless of the value of the variable, meaning the solution of the equation is all real numbers or that the equation has infinity solutions.
If instead, you get to a false statement. This means that the equation has no solution. This is because for no values of the variable the equation is true, and the equation is said to have no solutions.
In the end, always substitute your answer in original equation to check your answer.
Types of Linear Equations and steps to solve them
Single Step
You can solve equations using a single step of addition or subtraction.
Example:
x + 4 = 6
-4 -4 (subtract 4 on both sides)
x = 2
You can solve equations using a single step of addition or subtraction.
Example:
2x = 6
/2 /2 (divide by 2 on both sides)
x = 3
Multiple Step
You can solve equation by using multiple steps.
1. Simplify each side of the equation
2. If the side containing variable involves a certain order, apply the inverse operations in opposite order
Example:
3x + 4 = 7
-4 -4 (subtract 4 on both sides)
3x = 3
/3 /3 (divide by 3 on both sides)
x = 1
Multiple Step with Variables on both sides
If an equation has variables on both sides, use following steps to solve it:
1. Add or subtract a variable expression on both sides to isolate the variable terms on 1 side
2. Simplify each side of the equation
3. If the side containing variable involves a certain order, apply the inverse operations in opposite order
Example:
6x = 4x + 18
-4x -4x (subtract variable term 4x on both sides)
2x = 18
/2 /2 (divide by 2 on both sides)
x = 9
Multiple Step Equations with Fraction
If an equation has 1 or more terms with fractions, use following steps to solve it:
1. Write all terms in the equation as fraction
2. Multiply every term with the LCM of the denominator.
This will change all the terms in the equation to non-fraction form.
3. Add or subtract a variable expression on both sides to isolate the variable terms on 1 side
4. Simplify each side of the equation
5. If the side containing variable involves a certain order, apply the inverse operations in opposite order
Example:
coming soon...
Multiple Step Equations with Absolute values
If an equation has variables on both sides, use following steps to solve it:
1. Isolate the absolute value.
2. rewrite the absolute value equation as 2 separate equations - 1 positive and 1 negative.
3. Solve each equation separately.
4. Plug in both answers in the original equation to verify that your solutions are valid.
Example:
coming soon...
You can solve equations using a single step of addition or subtraction.
Example:
x + 4 = 6
-4 -4 (subtract 4 on both sides)
x = 2
You can solve equations using a single step of addition or subtraction.
Example:
2x = 6
/2 /2 (divide by 2 on both sides)
x = 3
Multiple Step
You can solve equation by using multiple steps.
1. Simplify each side of the equation
2. If the side containing variable involves a certain order, apply the inverse operations in opposite order
Example:
3x + 4 = 7
-4 -4 (subtract 4 on both sides)
3x = 3
/3 /3 (divide by 3 on both sides)
x = 1
Multiple Step with Variables on both sides
If an equation has variables on both sides, use following steps to solve it:
1. Add or subtract a variable expression on both sides to isolate the variable terms on 1 side
2. Simplify each side of the equation
3. If the side containing variable involves a certain order, apply the inverse operations in opposite order
Example:
6x = 4x + 18
-4x -4x (subtract variable term 4x on both sides)
2x = 18
/2 /2 (divide by 2 on both sides)
x = 9
Multiple Step Equations with Fraction
If an equation has 1 or more terms with fractions, use following steps to solve it:
1. Write all terms in the equation as fraction
2. Multiply every term with the LCM of the denominator.
This will change all the terms in the equation to non-fraction form.
3. Add or subtract a variable expression on both sides to isolate the variable terms on 1 side
4. Simplify each side of the equation
5. If the side containing variable involves a certain order, apply the inverse operations in opposite order
Example:
coming soon...
Multiple Step Equations with Absolute values
If an equation has variables on both sides, use following steps to solve it:
1. Isolate the absolute value.
2. rewrite the absolute value equation as 2 separate equations - 1 positive and 1 negative.
3. Solve each equation separately.
4. Plug in both answers in the original equation to verify that your solutions are valid.
Example:
coming soon...