8 - 9 solving equation strategies

Question 1

technique

7 ways for manipulating and solving equations

Answer 1

1. don’t forget to combine like terms
2. square and square root correctly
3. cross-multipy when fractions are set equal to each other
4. factoring should be in your tool box
5. treat complicated expressions as one unit
6. be comfortable solving for expressions, rather than any one variable
7. guess and check when you’re out of options

Question 2

recognizing types of questions

the same variables are on both sides of the equation

Answer 2

combine like terms

Question 3

recognizing types of questions

when a fraction is equal to another fraction

Answer 3

cross multiply

Question 4

recognizing types of questions

when variables are hard to isolate

Answer 4

expand everything and put every term containing the same variable to one side and factor and isolate that variable

Question 5

explanation

treat complicated expressions as

Answer 5

one unit or variable, such as A or B or C

Question 6

technique

when solving equations first

Answer 6

look for what you want before you solve for anything specific and ask the question:
is there any way to get the answer without solving for x and y?

Question 7

technique

if you have to do a question that is complicated without a calculator or any answer choices,

Answer 7

you know it has to be solvable through a basic guess and check

Question 8

technique

when doing guess and check,

Answer 8

use numbers like 0, 1, 2, and -1

Question 9

technique

2 equation solving strategies for tougher questions

Answer 9

1. matching coefficients
2. clearing denominators

Question 10

example

(x+a)^{2}=x^{2}+8x+b

Answer 10

1. expand left side of equation to find something meaningful
   (x+a)^{2}= x^{2} + 2ax + a^{2}
   2.** match up coefficients**
   x^{2} + 2ax + a^{2} = x^{2}+8x+b
2. solve
   2a = 8 –> a = 4
   a^{2} = b –> b = 16

Question 11

recognizing type of questions

when solving an equation with fractions with different denominators

Answer 11

get rid of the fractions by multiplying both sides by the common multiple of the denomiators

Question 12

example

3/x + 5/(x+2) = 2

Answer 12

1. multiply both sides by x(x+2)
   3/x * x(x+2) + 5/(x+2) * x(x+2)
   = 2