1-2 Solving linear Equations

Question 1

equivalent equation

Answer 1

equations that have the same solution

Question 2

inverse operations

Answer 2

undo each other

addition <-> subtraction
multiplication <-> division
squaring <-> square root
cubing <-> cube root

Question 3

isolate

Answer 3

get variable by itself on one side of equation

Question 4

solution of an equation

Answer 4

a value for the variable that makes the equation a true statement

Question 5

variable

Answer 5

an unknown quantity
a quantity that can vary

Question 6

How to eliminate fractions when solving equations

Answer 6

multiplying EVERY term by denominator of the fraction

what if denominators are different numbers?

find least common multiple and multiply all terms by it

EX 1 Solve Linear Equations

Question 7

Consecutive Odd Integers equations

Answer 7

1) define the variable
Let x = first odd consecutive integer
x + 1 = second odd consecutive integer
x + 2 = third odd consecutive integer

2) write equation
x + x + 1 + x + 2 = sum of three consecutive odd integers

3) solve

4) identify what the three consecutive odd integers are

EX 2 Solve Consecutive Integer Problems

Question 8

Consecutive Even Integer equations

Answer 8

1) define the variable
Let x = first consecutive even integer
x + 2 = second consecutive even integer
x + 4 = third consecutive even integer

2) write the equation
x + x + 2 + x + 4 = sum of first three consecutive even integers

3) solve

4) identify the three consecutive even integers

EX 2 Solve Consecutive Integer Problems

Question 9

Consecutive Integer equations

Answer 9

1) define the variable
Let x = first consecutive integer
x + 1 = second consecutive integer
x + 2 = third consecutive integer

2) write equation
x + x + 1 + x + 2 = sum of three consecutive integers

3) solve

4) identify the three consecutive integers

EX 2 Solve Consecutive Integer Problems

Question 10

How to check the solution?

Answer 10

Substitute the value of the variable into the equation.

If it makes the equation true, it is a solution to the equation.

EX 2 Solve Consecutive Integer Problems

Question 11

Mixture equations

Answer 11

1) define the variables
Let x = amount of first solution
Let total amount of mixture - x = amount of second solution

2) percents must be converted to decimals by moving the decimal two places to the left

3) write the equation
(% of first solution as decimal)(x) +
(% of second solution as a decimal)(total amount of mixture - x)
= (total amount of mixture)(% of mixture as a decimal)

4) solve

5) identify how much of first solution and how much of second solution will be needed

EX 3 Use Linear Equations to Solve Mixture Priblems