Objective 3 - Solve Compound Linear Inequalities

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Solve linear inequalities.

Link to section in online textbook.

Watch this video to learn how to solve compound inequalities. For both kinds of compound inequalities, we first split it into two inequalities, solve separately, then put them back together at the end.

$\sage {displayLeftFactor1A} < \sage {displayRightFactor1A}$ or $\sage {displayLeftFactor1B} > \sage {displayRightFactor1B}$

$\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer [tolerance=0.05]{\sage {solution1A[0][1]}} \answer [format=string]{)}$
$\cup$
$\answer [format=string]{(} \answer [tolerance=0.05]{\sage {solution1B[0][0]}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

There are four boxes so you can input the entire interval. Each interval should be:
( or [
number or $\infty$
number or $\infty$
) or ]

$\sage {displayLeftFactor2A} \leq \sage {displayRightFactor2A}$ or $\sage {displayLeftFactor2B} \geq \sage {displayRightFactor2B}$

$\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer [tolerance=0.05]{\sage {solution2A[0][1]}} \answer [format=string]{]}$
$\cup$
$\answer [format=string]{[} \answer [tolerance=0.05]{\sage {solution2B[0][0]}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

There are four boxes so you can input the entire interval. Each option should be:
( or [
number or $\infty$
number or $\infty$
) or ]

$\sage {andInequalityLeft3} < \sage {andInequalityMiddle3} < \sage {andInequalityRight3}$

$\answer [format=string]{(} \answer [tolerance=0.05]{\sage {smallerEndpoint3}}, \answer [tolerance=0.05]{\sage {largerEndpoint3}} \answer [format=string]{)}$

There are four boxes so you can input the entire interval. Each option should be:
( or [
number or $\infty$
number or $\infty$
) or ]

$\sage {andInequalityLeft4} \leq \sage {andInequalityMiddle4} \leq \sage {andInequalityRight4}$

$\answer [format=string]{[} \answer [tolerance=0.05]{\sage {smallerEndpoint4}}, \answer [tolerance=0.05]{\sage {largerEndpoint4}} \answer [format=string]{]}$

There are four boxes so you can input the entire interval. Each option should be:
( or [
number or $\infty$
number or $\infty$
) or ]

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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