Objective 2 - Solve Linear Inequalities - Ximera

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Solve linear inequalities.

Link to section in online textbook.

First, watch the video below to learn how to use the properties of inequalities to solve linear inequalities. You can use the notes here to follow along with the video and record your thoughts.

Now try to solve the different linear inequalities below.

$\sage {displayLeftFactor3} \leq \sage {displayRightFactor3}$

$\answer [format=string]{[} \answer [tolerance=0.05]{\sage {solution3[0][0]}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

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

$\sage {displayLeftFactor4} \geq \sage {displayRightFactor4}$

$\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer [tolerance=0.05]{\sage {solution4[0][1]}} \answer [format=string]{]}$

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

$\sage {displayLeftFactor5} < \sage {displayRightFactor5}$

$\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer [tolerance=0.05]{\sage {solution5[0][1]}} \answer [format=string]{)}$

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

$\sage {displayLeftFactor6} > \sage {displayRightFactor6}$

$\answer [format=string]{(} \answer [tolerance=0.05]{\sage {solution6[0][0]}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

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

$\sage {displayLeftFactor7} < \sage {displayRightFactor7}$

$\answer [format=string]{(} \answer [tolerance=0.05]{\sage {solution7[0][0]}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

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

$\sage {displayLeftFactor8} > \sage {displayRightFactor8}$

$\answer [format=string]{(} \answer [tolerance=0.05]{\sage {solution8[0][0]}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

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

$\sage {displayLeftFactor9} \leq \sage {displayRightFactor9}$

$\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer [tolerance=0.05]{\sage {solution9[0][1]}} \answer [format=string]{]}$

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

$\sage {displayLeftFactor10} \geq \sage {displayRightFactor10}$

$\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer [tolerance=0.05]{\sage {solution10[0][1]}} \answer [format=string]{]}$

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

Start typing the name of a mathematical function to automatically insert it.

(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)

Symbols

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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