1. (x - 3)(x + 3) = 27
Note: This pattern, (x - a)(x + a) should become familiar
to you. It always multiplies to x2 - a2, thus in
problem 1, (x -3)(x + 3) = x2 - 9
move the -9 to
the right side
2. x -3x + 2 - y = 0
Move the 2 to the right by subtraction
and the -y to the right by addition
(inverse operations!)
Divide both sides by -2.
How did I make the final step?
3. 5x - 4 = 21
Move the 4 to the right side by adding 4 to both sides.
Divide both sides by 5 to remove the 5 that multiplies the x.
4. x(x - 1) + x = 4
Distribute the x across the binomial (x-1)
x - x means no more x!
Take the square root of both sides to get x from x2
Don‛t forget the ±
5. 3x(x - 2) + 6x = 27
Distribute the 3x across the binomial (x-2)
The ±6x cancel one another, leaving zero.
Divide both sides by 3 to leave just the x2 term.
Take the square root of both sides.
© J. Cruzan, 2013
Solutions to web Algebra problems
Page 1 of 3
6. x2 - (x - 2)(x + 2) = 4
FOIL the (x-2)(x+2) to expand it
The ±2x cancel one another.
The minus sign between x2 and ( means to
multiply everything in parenthesis by -1
This strange result, “4 = 4” is always true. It means that
any x at all will satisfy this equation. No matter the value
of x chosen, the equation will always be true.
7. 3(x - 2) + 4(x - 2) = x
Distribute
Group like terms: containing x and constants
Move the 14 to the right by addition, the x to the left
by subtraction
8. x - 6 + 3(x - 2) = 12
10. 4(x - 1) - x(x - 1) = -x2
© J. Cruzan, 2013
9. 9x2 - 9(x - 3)2 = 27
11. -9x + 3y - z = 0
Solutions to web Algebra problems
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12. 6x + 121 = -5x
13. (x + 5)(x - 5) = 0
15. 2(x2 - 3x + 2) = 2(x - 1)(x + 1)
14. (x - a)(x + a) = 0
16. -4(x - 1) + 4(x - 1) = x
(x-1) is a common factor
17. 7(x2 - 3) = 7x2 - x
19. 4x2 = 64
18. x(x - 2) - 2x(x - 1) + x2 = x
20. -4x2 = 64
Actually, there is a solution, it‛s just
not a real number ... it‛s a “complex
number” ... more on that later.
© J. Cruzan, 2013
Solutions to web Algebra problems
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