50 Challenging Algebra Problems (Fully Solved) Chris McMullen Improve your Math Fluency Zishka Publishing

226 Pages·2019·19.52 MB·English

by  Chris McMullen

50 CHALLENGING
ALGEBRA PROBLEMS
(Fully Solved)
Improve Your Math Fluency
Chris McMullen, Ph.D.
Copyright © 2018 Chris McMullen, Ph.D.
www.improveyourmathfluency.com
All rights reserved. However, teachers or parents who purchase one copy of
this workbook (or borrow one physical copy from a library) may make and
distribute photocopies of selected pages for instructional (non-commercial)
purposes for their own students or children only.
Zishka Publishing
ISBN: 978-1-941691-23-6
Textbooks > Math > Algebra
Study Guides > Workbooks> Math
Education > Math > Algebra

Contents
Problems 1-5
Problems 6-10
Problems 11-15
Problems 16-20
Problems 21-25
Problems 26-30
Problems 31-35
Problems 36-40
Problems 41-45
Problems 46-50
ABOUT THE AUTHOR
Problem 1
Directions: Solve for x in the equation below. (Don’t use guess and check.)
• You can find the solution on the following page.
Solution to Problem 1
Subtract from both sides of the equation in order to isolate the
unknown term.
Square both sides of the equation to get the variable out of the squareroot.
Apply the rules and (a – b)2 = a2 – 2ab + b2 where
and .
Apply the rules and .
Note that 32 + 2 = 34 and (32)(2) = 64.
Note that .
x = 34 – (2)(8)
x = 34 – 16
x = 18
Check the answer: Plug x = 18 into the original equation.
Use a calculator.
4.242640687 + 1.414213562 = 5.656854249
The answer checks out.
Common mistake: It’s incorrect to rewrite
as x + 2 = 32. You can easily verify that x doesn’t equal 30 by plugging 30 in
for x in the original equation with a calculator. You can’t square each term
individually in algebra. You can square both sides of the equation, but then
you get a cross term when you f.o.i.l. it out:
That’s why x + 2 = 32 is incorrect. It should really be
Problem 2
Directions: Solve for x and y in the system of equations below.
• You can find the solution on the following page.