Steps to Solve Equations

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

• -cos²x = 0

• cosx(2cosx + 3) = 0

• cosx(2cosx − 3) = 0

• cos x = ⅔

Which is a correct way to solve the equation cosx(2cosx − 3) = 0?

• divide cos x from both sides

• set each factor equal to 0 and solve

• distribute cosx into the parentheses

• guess and hope for the best

Choose a good way to start solving this equation

tanx sin²x = 2 tanx

• divide tanx from both sides

• factor out tanx

• subtract 2 tanx from the left and then factor tanx out

• cancel sin²x out

To solve this equation, cos²x + sinx = 1, replace cos²x with

• 1/(sec²x)

• sin²x − 1

• 1 − sin²x

• 1 + tan²x

To solve the equation sec²x − secx = 2

• start by subtracting 2 from both sides and then factor

• add sec x to both sides and factor

• factor out secx and set each factor equal to 2

• sec x is never bigger than 1, so there are no solutions

Organize this equation so it can be factored:

1−sin²x + sinx = 1

• move all to the right: 0 = sin²x − sinx

• cancel the ones and cancel a sinx

• replace sin²x with 1 − cos²x

• use this: 0 = sin²x − sinx + 2

Solve the equation (secx − 2)(secx + 1) = 0 on [0, 360⁰)

• 60⁰, 180⁰, 300⁰

• 30⁰, 180⁰,330⁰

• 60⁰, 120⁰

• 180⁰

The objective when solving an equation is to....

• isolate the variable.

• check the solution.

• guess and check.

• Combine Like Terms.

What is a 2-step problem?

• An equation where 2 steps are needed to solve it.

• An equation where only one step is needed to solve it.

• A problem with only one operation present.

• A problem where you find the square-root of a number.

What is the inverse operation needed to solve the following one-step equation?
-11x = 121

• subtraction

• addition

• multiplication

• division