9.6 Techniques for Solving Equations and Inequalities
Chapter
Chapter 9
Section
9.6
Solutions 33 Videos

For each graph shown below, state the solution to each of the following:

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} f(x) = g(x) &(b) \phantom{.} f(x) \leq g(x) \\ &(c) \phantom{.} f(x) > g(x) &(b) \phantom{.} f(x) \geq g(x) \\ \end{array} Q1i

For each graph shown below, state the solution to each of the following:

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} f(x) = g(x) &(b) \phantom{.} f(x) \leq g(x) \\ &(c) \phantom{.} f(x) > g(x) &(b) \phantom{.} f(x) \geq g(x) \\ \end{array} Q1ii

Solve for x \in [0, 2]

\displaystyle 3 = 2^{2x} 

Q2a

Solve for x

\displaystyle 0 = \sin(0.25x^2)  when x \in [0, 5]

Q2b

Solve for x

\displaystyle 3x = 0.5x^3  when x \in [-8, -1]

Q2c

Solve for x

\displaystyle \cos x = x  when x \in [0, \frac{\pi}{2}]

Q2d

Solve for x when a) f(x) < g(x)

b) f(x) = g(x)

c) f(x) > g(x)

Q4

Solve using a graphing device. Q5a

Solve the following equations for x in the given interval, using a guess and improvement strategy. Express your answers to the nearest tenth.

 \displaystyle \sin^3x = \sqrt{x} -1, 0 \leq x \leq \pi 

Q5b

Solve for x.

 \sin(2\pi x) = -4x^2+ 16x - 12, 0 \leq x \leq 5 

Q5f  Coming Soon
Q6a  Coming Soon
Q6b  Coming Soon
Q6c  Coming Soon
Q6d  Coming Soon
Q6e  Coming Soon
Q6f  Coming Soon
Q7 Q8 Coming Soon
Q9a Coming Soon
Q9b Coming Soon
Q9c Coming Soon
Q9d Coming Soon
Q9e Coming Soon
Q9f Q10 Q11 Q12 Coming Soon
Q13 Q14 Q15
Lectures 6 Videos

Solving inequalities in Composite Functions.

ex. Solve for x for
 \displaystyle \log_2(x + 1) > 2 

1.05mins
Introduction to Inequality

ex. Solve for x for

 \displaystyle [\log_2(x - 1)]^2 - 2\log_2(x - 1) > 0 

1.06mins

ex. Solve for x for

 \displaystyle 2^{\log_2(x + 2)}> 27 

2.04mins
Exponent Form Inequality

ex. Solve for x for

 \displaystyle 1 \leq \log_2(x^2 - 1) \leq 3 

3.10mins
Log between Two Values

ex. Find the inverse of

 \displaystyle y = 2^{3^{x - 1}} + 3 

 \displaystyle f(x) = -3\log_3\log_2(x + 5) + 2  and find the range of f(x).