Introduction to Solving Linear Equations A Calder mobile is balanced and has several elements on each side. (credit: paurian, Flickr)
Teetering high above the floor, this amazing mobile remains aloft thanks to its carefully balanced mass. Any shift in either direction could cause the mobile to become lopsided, or even crash downward. In this tutorial, we will solve equations by keeping quantities on both sides of an equal sign in perfect balance.
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\( a^{b}\)
\( a_{b}^{c}\)
\({a_{b}}^{c}\)
\(a_{b}\)
\(\sqrt{a}\)
\(\sqrt[b]{a}\)
\(\frac{a}{b}\)
\(\cfrac{a}{b}\)
\(+\)
\(-\)
\(\times\)
\(\div\)
\(\pm\)
\(\cdot\)
\(\amalg\)
\(\ast\)
\(\barwedge\)
\(\bigcirc\)
\(\bigodot\)
\(\bigoplus\)
\(\bigotimes\)
\(\bigsqcup\)
\(\bigstar\)
\(\bigtriangledown\)
\(\bigtriangleup\)
\(\blacklozenge\)
\(\blacksquare\)
\(\blacktriangle\)
\(\blacktriangledown\)
\(\bullet\)
\(\cap\)
\(\cup\)
\(\circ\)
\(\circledcirc\)
\(\dagger\)
\(\ddagger\)
\(\diamond\)
\(\dotplus\)
\(\lozenge\)
\(\mp\)
\(\ominus\)
\(\oplus\)
\(\oslash\)
\(\otimes\)
\(\setminus\)
\(\sqcap\)
\(\sqcup\)
\(\square\)
\(\star\)
\(\triangle\)
\(\triangledown\)
\(\triangleleft\)
\(\Cap\)
\(\Cup\)
\(\uplus\)
\(\vee\)
\(\veebar\)
\(\wedge\)
\(\wr\)
\(\therefore\)
\(\left ( a \right )\)
\(\left \| a \right \|\)
\(\left [ a \right ]\)
\(\left \{ a \right \}\)
\(\left \lceil a \right \rceil\)
\(\left \lfloor a \right \rfloor\)
\(\left ( a \right )\)
\(\vert a \vert\)
\(\leftarrow\)
\(\leftharpoondown\)
\(\leftharpoonup\)
\(\leftrightarrow\)
\(\leftrightharpoons\)
\(\mapsto\)
\(\rightarrow\)
\(\rightharpoondown\)
\(\rightharpoonup\)
\(\rightleftharpoons\)
\(\to\)
\(\Leftarrow\)
\(\Leftrightarrow\)
\(\Rightarrow\)
\(\overset{a}{\leftarrow}\)
\(\overset{a}{\rightarrow}\)
\(\approx \)
\(\asymp \)
\(\cong \)
\(\dashv \)
\(\doteq \)
\(= \)
\(\equiv \)
\(\frown \)
\(\geq \)
\(\geqslant \)
\(\gg \)
\(\gt \)
\(| \)
\(\leq \)
\(\leqslant \)
\(\ll \)
\(\lt \)
\(\models \)
\(\neq \)
\(\ngeqslant \)
\(\ngtr \)
\(\nleqslant \)
\(\nless \)
\(\not\equiv \)
\(\overset{\underset{\mathrm{def}}{}}{=} \)
\(\parallel \)
\(\perp \)
\(\prec \)
\(\preceq \)
\(\sim \)
\(\simeq \)
\(\smile \)
\(\succ \)
\(\succeq \)
\(\vdash\)
\(\in \)
\(\ni \)
\(\notin \)
\(\nsubseteq \)
\(\nsupseteq \)
\(\sqsubset \)
\(\sqsubseteq \)
\(\sqsupset \)
\(\sqsupseteq \)
\(\subset \)
\(\subseteq \)
\(\subseteqq \)
\(\supset \)
\(\supseteq \)
\(\supseteqq \)
\(\emptyset\)
\(\mathbb{N}\)
\(\mathbb{Z}\)
\(\mathbb{Q}\)
\(\mathbb{R}\)
\(\mathbb{C}\)
\(\alpha\)
\(\beta\)
\(\gamma\)
\(\delta\)
\(\epsilon\)
\(\zeta\)
\(\eta\)
\(\theta\)
\(\iota\)
\(\kappa\)
\(\lambda\)
\(\mu\)
\(\nu\)
\(\xi\)
\(\pi\)
\(\rho\)
\(\sigma\)
\(\tau\)
\(\upsilon\)
\(\phi\)
\(\chi\)
\(\psi\)
\(\omega\)
\(\Gamma\)
\(\Delta\)
\(\Theta\)
\(\Lambda\)
\(\Xi\)
\(\Pi\)
\(\Sigma\)
\(\Upsilon\)
\(\Phi\)
\(\Psi\)
\(\Omega\)
\((a)\)
\([a]\)
\(\lbrace{a}\rbrace\)
\(\frac{a+b}{c+d}\)
\(\vec{a}\)
\(\binom {a} {b}\)
\({a \brack b}\)
\({a \brace b}\)
\(\sin\)
\(\cos\)
\(\tan\)
\(\cot\)
\(\sec\)
\(\csc\)
\(\sinh\)
\(\cosh\)
\(\tanh\)
\(\coth\)
\(\bigcap {a}\)
\(\bigcap_{b}^{} a\)
\(\bigcup {a}\)
\(\bigcup_{b}^{} a\)
\(\coprod {a}\)
\(\coprod_{b}^{} a\)
\(\prod {a}\)
\(\prod_{b}^{} a\)
\(\sum_{a=1}^b\)
\(\sum_{b}^{} a\)
\(\sum {a}\)
\(\underset{a \to b}\lim\)
\(\int {a}\)
\(\int_{b}^{} a\)
\(\iint {a}\)
\(\iint_{b}^{} a\)
\(\int_{a}^{b}{c}\)
\(\iint_{a}^{b}{c}\)
\(\iiint_{a}^{b}{c}\)
\(\oint{a}\)
\(\oint_{b}^{} a\)
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I would love to know more about this topic
M interested in this class and I would love you to explain to me every aspect of this topic.
Thanks you.