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Algebra: Difference between revisions
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→How to solve an equation
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** <math>x + 0 = 5</math> | ** <math>x + 0 = 5</math> | ||
**<math>x = 5</math> | **<math>x = 5</math> | ||
=== Operation === | |||
= a process to change a value | |||
* addition, subtraction, multiplication and division are the fundamental "operations" of math | |||
* | |||
===Property=== | ===Property=== | ||
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* an unknown value represented, usually represented by the letter <math>x </math> | * an unknown value represented, usually represented by the letter <math>x </math> | ||
==How to solve an equation== | ==How to solve an equation with a single variable== | ||
===Using Addition Property=== | ===Using Addition Property=== | ||
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|} | |} | ||
=== Cross-multiplying | === Cross-multiplying === | ||
<math> | * use cross-multiplication to solve for <math>x </math> when <math>x </math> is a denominator (bottom of a fraction) | ||
* | * see for numerators and denominators | ||
==== How to solve for <math>x </math> when <math>x </math> is a denominator: "Cross-multiplication" ==== | ==== How to solve for <math>x </math> when <math>x </math> is a denominator: "Cross-multiplication" ==== | ||
{| style="text-align: center;" | {| style="text-align: center;" | ||
|+Using Cross- | |+Using Cross-Multiplication | ||
!<math>\frac 6 x = 8 </math> | !<math>\frac 6 x = 8 </math> | ||
!is the same as | !is the same as | ||
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|- | |- | ||
| | | | ||
|now we can solve for <math>x</math> | |||
| | | | ||
| | |- | ||
|<math>8x= 6 \times 1 </math> | |||
|<math>8x= 16 </math><math>\frac {8\times x} 8 = \frac {16} 8 </math><math>x = \frac {16} 8 | |||
</math> | |||
|<math>x=2 | |||
</math> | |||
|} | |} | ||
== How to solve an equation with two of the same variables == | |||
* when an equation has two of the same variables, we isolate the variable by combining its instances | |||
* ex. | |||
** <math>2x + 5x = 35</math> | |||
** the values <math>2x | |||
</math> and <math>5x | |||
</math> may be "distributed" in order to make a single instance of <math>x | |||
</math> and thereby allowing for it to be isolated | |||
=== Distributive property === | |||
= the idea that multiplication can be "distributed" through addition | |||
* multiplication is addition by a certain factor (number of times) | |||
* ex. when we multiply <math>5 \times 5</math>, we are adding 5 five times: <math>5\times 5 = 5+5+5+5+5 | |||
</math> | |||
** that is the same as adding <math>(2+3)</math> five times | |||
** so we can express <math>(2+3)</math> times 5 as either | |||
*** <math>5 \times (2+3) | |||
</math> or | |||
*** <math>5 \times (5) | |||
</math> or | |||
*** <math>(5\times 2) + (5 \times 3) | |||
</math> | |||
**** they all equal 25 | |||
* with variables, we use the process: | |||
** <math>2x + 5x</math> = | |||
** <math>x \times (2+5) | |||
</math> = | |||
** <math>x \times 7 | |||
</math> = 7<math>x | |||
</math> | |||
[[Category:Math]] | [[Category:Math]] | ||