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
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).