Solving Equations II

Lesson 7.04

After completing this lesson, you will be able to say:

• I can solve one-variable equations containing multiplication or division.

• I can define and apply inverse operations of multiplication or division.

• I can solve real-world problems by writing and solving equations.

Solving Equations using the Inverse

Using inverse operations is a direct way to solving equations

What you do to one side of an Equation, you MUST do to the other side of the equation.

Remember the golden rule for solving equations:

Using the Inverse

The inverse operation of multiplication is division.

To "undo" multiplication in an equation you must divide the number on both sides of the equation to isolate the variable.

Using the Inverse - Example

Use inverse operations to solve the equation 10k = 60 for k.

The equation has k being multiplied by 10. To get k alone on the left side of the equal sign, you must use the inverse operation of multiplication. So, divide both sides of the equation by 10.

Next, cancel the common factors in the numerator and denominator, then simplify the equation.

Therefore, the solution to the equation 10k = 60 is k = 6.

Using the Inverse – Try It

Solve the equation 4.2x = 28.56 for x using inverse operations

Golden Rule for Solving Equations

What you do to one side of an Equation, you MUST do to the other side of the equation.

To solve an equation you must isolate the variable on one side of the equal sign by using inverse operations. This results in zero by undoing the operation

Example

Solve the equation x − 7 = 18 to determine the value of x.

To determine the value of x, you must isolate it on one side of the equation. Use inverse operations to get the variable alone.

Operations Explanation

x − 7 = 18

x − 7 + 7 = 18 + 7 Use the inverse operation of subtraction by adding 7 to both sides of the equation and simplify.

X = 25 The solution to the equation is 25.

Using the Inverse – Check your work

Solve the equation 4.2x = 28.56 for x using inverse operations

Using the Inverse

The inverse operation for division is multiplication. If an equation has a coefficient that is a fraction, you just multiply both sides of the equation by the reciprocal of that coefficient.

Using the Inverse - example

Using the Inverse - example

Using the Inverse – Try it

Using the inverse – check your work

Now that you completed this lesson, you should be able to say:

• I can solve one-variable equations containing multiplication or division.

• I can define and apply inverse operations of multiplication or division.

• I can solve real-world problems by writing and solving equations.