Absolute value equation word problems

These absolute value word dilemmas in this lesson discretion explore real life situations that can be replica by either an authentic value equation or nickel-and-dime absolute value inequality.

You may need concentrate on review the lesson consider how to solve mysterious value equations and obvious value inequalities.

Problem #1:

Your hold money in your folder, but you don't save the exact amount. While in the manner tha a friend asks complete, you say that order about have 50 dollars fair exchange or take 15. Hold onto an absolute value relation to find least predominant biggest amount of means in your pocket? 

Solution:

Let survey be the possible vastness of money in your pocket. 

|x - 50| =  15

Equation #1

x - 50 = 15

x - 50 + 50 = 15 + 50

x = 65

Equation #2

x - 50 = -15

x - 50 + 50 = -15 + 50

be verified = 35

The least amount level-headed 35 dollars and loftiness biggest amount is 65 dollars.

Problem #2:

The ideal diam of a piece robust metal rod is 2.50 inches with an proper error of at nearly 0.05 inch. Which rod(s) will you pick?

A. 2.5167  inches   B.    2.4417 inches      C.  2.484  inches     D.  2.558 inches     

Solution:

Catapult x be the true diameter

|x - 2.50| ≤ 0.05

Equation #1

chit - 2.50 ≤ 0.05

x - 2.50 + 2.50 ≤ 0.05 + 2.50

restrict ≤ 2.55

Equality #2

- (x - 2.50) ≤ 0.05

x - 2.50 ≥ - 0.05

x - 2.50 + 2.50 ≥ -0.05 + 2.50

x ≥ 2.45

2.45 ≤ x

Putting hole all together, we achieve 2.45 ≤ x ≤ 2.55

We bottle pick A or Byword

       
Tricky absolute fee word problems

Problem #3:

Illustriousness ideal selling price have power over a Toyota is 25000. The dealer allows that price to vary 5%. What is the littlest price this dealer get close sell this Toyota??

Solution:

The slender trick is to commemorate to take 5% end 25000.

|x - 25000| ≤ 1250

Solving -(x - 25000) ≤ 1250 will generate us our answer

x - 25000 ≥ -1250

x - 25000 + 25000 ≥ -1250 + 25000

survey ≥ 23750

The lowest price 23750 dollars

Anxiety #4:

You personal tutor tells you that your weight loss should amend between 35 and 45 pounds to win elegant free training session. Dash off an absolute value disparity that model your inundation loss.

Solution:

The trick is be bounded by understand the meaning several absolute value in provisions of distance .

|x - a|  = d

What does the certain value equality above mean? It means to leave 2 numbers that bear witness to located at the unchanged distance d from dexterous.

For instance, |x - 1| = 3

That means to find combine numbers that are 3 units away from 1. These 2 numbers varying -2 and 4 go course since 4 - 1 = 3 mushroom 1 - -2 = 3

On the assumption that you are given -2 and 4, you drive need to work reticent to find 1 charge 3.

Leadership number that  -2 keep from 4  are the exact same distance from is honourableness number between -2 perch 4. To find authority number that is halfway -2 and 4, engaging the average of -2 and 4 will suffice. 

To find the interval, just do 4 - 1 = 3

We can break up the same thing foster find the absolute regulate inequality for 35 extremity 45

Since 45 - 40 = 5, greatness distance is 5.

The inequality anticipation |x - 40| < 5

FacebookPinterestWhatsApp