In this lesson, we will learn how to solve equations using multiplication and division. This method involves multiplying or dividing both sides of the equation by a constant to isolate the variable.
To solve an equation using multiplication and division, follow these steps:
Step 1: Simplify both sides of the equation if necessary.
Step 2: Determine whether you need to multiply or divide both sides of the equation to isolate the variable. This depends on the operation being used to connect the variable and the constant or constants.
If the operation is addition or subtraction, use multiplication to isolate the variable. Multiply both sides of the equation by a constant so that the constant on the side with the variable cancels out.
If the operation is multiplication or division, use division to isolate the variable. Divide both sides of the equation by a constant so that the constant on the side with the variable cancels out.
Step 3: Simplify both sides of the equation again if necessary.
Step 4: Solve for the variable by following the order of operations.
Examples:
Example 1: Solve the equation 3x = 15 using multiplication.
Step 1: The equation is already simplified.
Step 2: Since the operation connecting the variable and the constant is multiplication, we will use division to isolate the variable. Divide both sides of the equation by 3.
3x/3 = 15/3
x = 5
Step 3: The equation is already simplified.
Step 4: The solution is x = 5.
Example 2: Solve the equation 2y + 10 = 25 using multiplication.
Step 1: The equation is already simplified.
Step 2: Since the operation connecting the variable and the constant is addition, we will use multiplication to isolate the variable. Multiply both sides of the equation by 2.
2(2y + 10) = 2(25)
4y + 20 = 50
Step 3: The equation is already simplified.
Step 4: Solve for y by subtracting 20 from both sides.
4y + 20 - 20 = 50 - 20
4y = 30
Divide by 4 to isolate y.
4y/4 = 30/4
y = 7.5
Step 5: The solution is y = 7.5.
Remember to always simplify both sides of the equation after each step and to follow the order of operations when solving for the variable.
Unit 4 lesson 3 solving equations using multiplication and division
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