Video Lessons > Solving Equations with Multiplication
Introduction and Video
Solving equations with multiplication involves understanding the different representations of multiplication and using the opposite operation to isolate the variable. This video lesson will walk through the step-by-step process of solving equations with multiplication and checking the correctness of the answer.
Recognizing Equations with Multiplication
When working with equations involving multiplication, it's important to recognize the different ways multiplication can be represented.
Multiplication can be represented by numbers next to parentheses, indicating multiplication of the number by the content within the parentheses.
A number written next to a variable with no symbol between them represents the coefficient of the variable, signifying that they are being multiplied together.
Take note of negative coefficients to ensure that the negative sign is not mistaken for a subtraction sign.
Lesson Notes
Let's look at the steps for solving equations with multiplication.
Example 1: Solving 7m = 63
Let's consider an example equation "7m = 63" to illustrate the step-by-step process of isolating the variable m and solving the equation. Notice that 7 is next to the variable, indicating multiplication.
Set Up the Equation: Draw a line down through the equal sign to clearly see the left and right sides of the equation.
Undo: Undo the multiplication by using the opposite operation, which in this case is division. Divide both sides of the equation by the coefficient of 7. This will help us isolate the variable m.
Simplify: Simplify both sides of the equation after dividing by 7. The result gives us m = 9.
Check: Check the correctness of the solution by substituting the value of the variable back into the original equation and simplifying it. If the resulting equation is true, the solution is correct.
Example 2: Solving -8b = 24
Next, we will break down the process of solving the equation -8b = 24 step by step to isolate the variable b.
Set Up: Before we start to solve the equation, it is important to recognize that the negative sign does not represent subtraction in this context, but it represents the sign of the number it is attached to. And don't forget to draw a line to separate each side of the equation!
Undo: To begin isolating the variable b, we need to perform the opposite operation to undo the effect of the multiplying by -8. This involves dividing by -8 on both sides of the equation. When dividing by -8, it is important to include the negative sign with the number.
Simplify: After dividing by -8, the left side of the equation simplifies to b, while the right side simplifies to -3. This results in the equation being transformed to b = -3.
Check: Lastly, we check the accuracy of the solution. When we substitute -3 for b in the original equation, we can see that it results in a true equation.
Summary and Practice
In this video lesson, we explored a systematic approach for solving equations with multiplication. By understanding the different representations of multiplication and using the opposite operation of division, we can successfully isolate the variable and solve the equation. Be mindful of negative coefficients so that you know how to solve the equation properly. And always check the solution!
Try this practice activity to see what you learned. Complete the steps of this equation by dragging each element on the right to its correct place.
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