Solving Single and Double Step Equations Lesson

Single step equations are equations that we can solve using only one step, either addition, subtraction, multiplication, or division. Double step equations are equations that take exactly two steps to solve, using two of the operations mentioned previously. To solve equations we apply the inverse operation that is currently being applied to the variable. For example, if a variable is being multiplied by a number, in order to solve the equation we would divide both sides by the number in order to solve the equation.

An example of a single step equation, would be x + 3 = 8. We would solve this by subtracting 3 from both sides of the equation to keep the equation balanced. Therefore the answer would be x = 5. An example of a double step equation would be 2x- 4 = 8. We would add 4 to both sides to get 2x = 12, and then need to divide both sides by 2, to get the solution x = 6.

When solving single and double step equations we have to remember to “undo” the order of operations. In order words when we solve equations we are doing the order of operations in reverse. We always undo addition or subtraction first, then undo multiplication or division, and so on.

Single Step and Double Step Equations do not only have to be linear equations, and they can also involve integers, decimals or fractions. We will look at several various examples to get a good idea of what it means and how to solve single and double step equations.

When solving equations we must isolate the variable using the inverse of the operation currently being applied.

Steps for Solving Single Step Equations with Addition or Subtraction

Isolate the Variable

Add or subtract the constant term to move the term to the opposite side of the equation.

For example, in the equation x + 4, we would subtract 4 from both sides.

(1) x + 4- 4 = 9-4,which simplifies to x = 5.

Steps for Solving Single Step Equations with Multiplication or Division

Isolate the Variable

Multiply or divide the coefficient to move the term to the opposite side of the equation.

For example, in the equation y/5 = 3, we would multiply both sides by 5.

5 x y/5 = 3 x 5, which simplifies to y = 15.

Steps for Solving Single Step Equations with Fractions

Isolate the Variable

Multiply by the reciprocal of the fraction on both sides of the equation.

For example, in the equation, 3/4y = 6, we would multiply both sides by 4/3.

4/3 x 3/4y = 6 x 4/3, which simplifies to x = 8.

Steps for Solving Double Step Equations

Isolate the Variable Term

Add or Subtract the constant term to move the term to the opposite side of the equation.

For example: 2x + 7 = 13, 2x is the variable term, therefore we will subtract 7 from both sides.

2x + 7- 7 = 13- 7, which simplifies to 2x = 6.

Isolate the Variable

Multiply or Divide by the coefficient to isolate the variable.

In the example: 2x = 6, we would divide both sides by 2. 2x/2 = 6/2, which simplifies to x = 3.

Tips and Hints for Solving Equations

Perform Operations on Both Sides: Whatever operation is performed on one side of the equation, it must be done to the other side to maintain balance.

Combine Like Terms: Simplify expressions by combining like terms before isolating the variable.

Check Your Solution: Always check if the solution satisfies the original equation by substituting it back in.

Inverse Operations: Use inverse operations (opposite operations) to isolate the variable.

These steps provide a general guide, but practice is crucial for mastering the skills of solving equations.

Examples

Example 1: Solve the single step equation x + 8 = 12

Solution: Since 8 is added to the variable x, we will subtract (inverse of addition) 8 from both sides of the equation.

Therefore, the answer to the equation is x = 4.

Example 2: Solve the double step equation 3x + 5 = 26.

Solution: First we have to isolate the variable term, since the 5 is being added to the 3x, we will subtract (inverse of addition) 5 from both sides of the equation.

The first step simplifies the equation to 3x = 21, since the 3 is being multiplied by the variable x, we will divide (inverse of multiplication) 3 from both sides of the equation.

Therefore, the solution to the equation is x = 7.

Example 3: Solve the double step equation 2/3x – 4 = 6

Solution:

First we have to isolate the variable term, since the 4 is being subtracted from the variable term, we will add (inverse of subtraction) 4 to both sides of the equation.

The next step is to multiply both sides by the reciprocal of the fraction, which is the inverse of the given coefficient.

Therefore, the solution to the equation is x = 15.

FAQs on Solving Single and Double Step Equations

1) What is a single-step equation?

A single-step equation is an algebraic equation that can be solved in one operation. It involves isolating the variable by performing one main mathematical operation. An example of a single-step equation would be x + 8 = 4.

2) What is a double-step equation?

A double-step equation is an algebraic equation that requires two main operations to isolate the variable. It involves two steps to reach the solution. An example would be 3x + 5 = 14.

3) Are there key tips for solving equations?

Yes, key tips include performing operations on both sides of the equation, combining like terms, checking the solution, and using inverse operations to isolate the variable.

4) Do I always need to perform the same operation on both sides of the equation?

Yes,you must keep the equation balanced. Whatever operation is performed on one side, it must be done to the other side to keep the equation balanced, this is crucial in finding the correct answer.

5) How do I know which operation to perform first in a double-step equation?

Follow the order of operations in reverse order. Typically, it involves isolating variable terms first and then isolating the variable itself.

6) Why is it important to check the solution?

Checking the solution ensures that it satisfies the original equation. It helps catch errors and verifies the correctness of your solution.

7) How do I check my solution?

It is as simple as plugging your solution back into the original equation and simplifying to make sure it is correct.

8) What are inverse operations?

Inverse operations are opposite operations. For example, addition and subtraction are inverse operations, and multiplication and division are inverse operations.