9.1: X for Unknown
Look at the equation below. Can you figure out the value of ? In this concept, you will learn how to solve equations using the order of operations, distributive property, and square roots.
Guidance
The order of operations tells us the correct order of evaluating math expressions. We always do parentheses first . Then we do exponents . Next we do multiplication and division (from left to right) and finally addition and subtraction (from left to right) . The distributive property allows us to remove parentheses when there is an unknown inside of them.
In order to evaluate expressions using the distributive property and the order of operations, we can use the problem solving steps to help.
- First, describe what you see in the problem. What operations are there?
- Second, identify what your job is. In these problems, your job will be to solve for the unknown.
- Third, make a plan . In these problems, your plan should be to use the distributive property and the order of operations to get the by itself. At the end, you will use a square root.
- Fourth, solve .
- Fifth, check . Substitute your answer into the equation and make sure it works.
Example A
Solve for the positive value of . Show all steps.
Solution:
We can use problem solving steps to help us to solve this equation.
Example B
Solve for the positive value of . Show all steps.
Solution:
We can use problem solving steps to help us to solve this equation.
Example C
Solve for the positive value of . Show all steps.
Solution:
We can use problem solving steps to help us to solve this equation.
Concept Problem Revisited
We can use problem solving steps to help us to solve this equation.
Vocabulary
The order of operations tells us the correct order of evaluating math expressions. We always do parentheses first . Then we do exponents . Next we do multiplication and division (from left to right) and finally addition and subtraction (from left to right) . The distributive property allows us to remove parentheses when there is an unknown inside of them. The square root of a number is a value that, when multiplied by itself, gives the original number.
Guided Practice
Solve for the positive value of . Show all steps.
1.
2.
3.
Answers:
1. . Here are the steps to solve:
2. . Here are the steps to solve:
3. . Here are the steps to solve:
Practice
Solve for the positive value of . Show all steps.
Image Attributions
Description
Learning Objectives
Students apply the distributive property, use the order of operations, and take square roots to find the values of unknowns. Students willuse problem solving steps to help.