Determining absolute value inequalities

Assignment Help Algebra

Reference no: EM13117600

What is the best method for solving absolute value inequalities?

The first most important part about solving absolute value inequalities is to understand that there are two types of inequalities. These are |ax+b|<c and |ax+b|>c. These inequalities have totally different solutions. This is because of the difference between the two basic inequalities |x|<c and |x|>c. Absolute value is distance from 0. If |x|<c this means that the distance between x and 0 must be less than c. So then x must be between -c and c and we get a single interval (-c,c). If |x|>c, then the distance between x and 0 is greater than c. So x is either far away from 0 to the left or far away from 0 to the right. Now there are 2 intervals: (-infinity,-c) ; (c,infinity). We show how to "see" and solve these 2 types step-by-step.

Finally, we remember that |x|=|-x|. This means that we do not solve absolute value inequalities with a negative x inside! We simply rewrite it: |2-3x|=|3x-2|. This means we never have to worry about dividing by a negative number.

Reference no: EM13117600

Questions Cloud

Estimating quadratic equation : How many possible solutions are there to any quadratic equation? How can you tell the number of solutions there will be to any polynomial? Provide an example to support your answer.

How many grams of the nonvolatile solute glycerol must added : The vapor pressure of pure methanol, CH3OH, at 30 C is 160. torr. How many grams of the nonvolatile solute glycerol, C3H5(OH)3, must be added to 131. g of methanol to obtain a solution with a vapor pressure of 133. torr.

Verbal breakdown of step : What are the similarities and differences between the procedures needed to solve each of the following problems? Show your work and include a verbal breakdown of each step.

Illustrate what is the magnitude of the footballs resultant : At the point he throws a 50.0 yards forward pass straight down the field. Illustrate what is the magnitude of the football's resultant displacement?

Determining absolute value inequalities : What is the best method for solving absolute value inequalities? Finally, we remember that |x|=|-x|. This means that we do not solve absolute value inequalities with a negative x inside! We simply rewrite it: |2-3x|=|3x-2|. This means we never have..

Illustrate what are the velocities of the two people : Illustrate what are the velocities of the two people after the snowball is exchanged? Disregard the friction between the skates and the ice.

Algebra-equation of line : Find the equation in standard form of the straight line that passes through the point midway between (-7, -12) and (-5, 2) and has a slope of 3.

Equation that contains radical expressions : Does every equation that contains radical expressions have a solution? Provide an example with your explanation.

Illustrate what is the magnitude of the force : accelerates it to the right. It is observed that it takes the box 3.7 seconds to travel 61 meters. Illustrate what is the magnitude of the force?

User Account

All Pages