By Mr. Graham The Wonderful And Magnificent. Aka El Capitan

By Mr. Graham the wonderful and magnificent. AKA El Capitan

Solving Inequalities with Rational Numbers 

Even George is figuring this out. THERE ARE NO RULE CHANGES! EVERYTHING IS THE SAME. SOLVE LIKE NORMAL EXCEPT WE HAVE AN INEQUALITY SYMBOL INSTEAD OF AN EQUAL SIGN!

Solving Inequalities with Rational Numbers (decimals)  0.5x ≥

0.5  What operation is being done?  0.5x ≥ 0.5  0.5 0.5 divide both sides by 0.5 x≥

1

Solving Inequalities with Rational Numbers (decimals) t–

7.5 < 30  Opposite of subtraction is addition  t – 7.5 + (7.5) < 30 + (7.5)  t < 37.5

Solving Inequalities with Rational Numbers (fractions) x+

<1  Opposite of addition is subtraction x+ < 1– x<

Solving Inequalities with Rational Numbers (fractions)     



First, always change mix #s to improper fractions What operation is happening? Undo multiplication with division. Remember to divide fractions, multiply by the reciprocal. 1

=

-1 Because we divided by a negative #, what happens to my inequality sign?  So we have y < -3



Solving Inequalities with Rational Numbers 

With first-class mail, there is an extra charge in any of these cases:  The length is greater than 11 ½ inches  The height is greater than 6 1/8 inches  The thickness is greater than ¼ inch  The length divided by the height is less than 1.3 or

greater than 2.5 The height of an envelope is 4.5 inches. What are the minimum and maximum lengths to avoid an extra charge? List the important information. The height is 4.5 inches and if the length divided by the height is between 1.3 and 2.5, there will not be an extra charge.

Solving Inequalities with Rational Numbers  Show the  1.3

≤

 Solve

relationship ≤ 2.5

two problems

 1.3

≤  4.5 · 1.3 ≤  5.85 ≤

· 4.5

Solving Inequalities with Rational Numbers  And

 So

5.85 ≤ length ≤ 11.25  The length of the envelope must be greater than 5.85 inches but less than 11.25 inches to not have an extra charge.

practice

practice

Practice