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Unit OverviewIn this unit, you will use the procedure to solve multi-step equations to solve multi-step inequalities and graph solutions on the number line. You will then examine how to convert measurements using dimensional analysis, a method used often in scientific studies. The study of measurement ends with a look at the exactness of a measurement and how to allow for variances. Solving Multi-step Inequalities
Solving Inequalities (04:12)
*When multiplying or dividing by a negative number, the inequality sign must be reversed.Let’s take a look at why this rule applies. Let’s say that we know 4 > 2. If we multiply both sides of this inequality by a –2, let’s see what happens to the inequality.
You can represent the solution of an inequality in one variable on a number line. For < and > an open circle is used to denote that the solution number is not included in the solution.For ≤ and ≥ a closed circle is used to denote that the solution number is included in the solution.
Stop! Go to Questions #1-9 about this section, then return to continue on to the next section.Measurement In the real world, measurements can seldom be exact. Sometimes, it is impossible to measure exactly because of the measurement tool. Other times, it is simply more expedient (easier) not to use an exact measurement. This gives us three types of measuring:
What type of measurement is used to determine the amount of material to order? Estimation because they just needed an estimate to order the material.
What type of measurement is used to determine the amount that will be collected? Exact, both numbers are used to state an exact amount determined.
What type of measurement is used? Approximation, this is as accurate as the measuring tape will show.
Note: In determining the type of measurement, another factor considered is that the measurement is accurate enough to make the design on the computer.Exact Number Needed -- Steel Beams (04:12) Adequate Estimates -- Wedding Food (01:12) Flexibility -- Travel Budget (01:59) Stop! Go to Questions #10-12 about this section, then return to continue on to the next section.Relative Error Because no measurement is “exact,” we will examine how to find the relative error. is the ratio of the absolute value of the difference of a measured value and and actual value, compared to the actual value.
Relative error When relative error is expressed as a percent, it is called percent error. *Note: The absolute value sign is used to provide a positive amount because we are not concerned if the value is over or under the actual value. When dealing with measurements, the greatest possible error it is always of the unit in both directions.
Find the differences:
Use the GREATER possible difference to compute the relative error. In this example, the greater difference in area is 13.25.Introduction: Error in Foam Making (01:57) Absolute and Relative Error -- Construction (03:02) Importance of Errors -- Emergency Room (01:58) Low Tolerance for Error -- Drag Racing (01:45) By changing the ratio to a percent we can see the greatest possible percent error in area, based on measurements to the nearest foot, is about 8%. Stop! Go to Questions #13-15 about this section, then return to continue on to the next section.Measurement Conversions Study the below example of using conversion factors to accurately compare or convert units.
Practice Problem: Unit Conversion Factors (01:07) Performing Multiple Unit Conversions (03:50) Practice Problems: Unit Conversions (05:22) Go to Questions #16-26 to complete this unit.Stop! |

Multi-step Inequalities |

Measurement Conversions |