Question 174957
Hi, Hope I can help,
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how do i find the value of x in the equation {{{ x/2+20=15+x/3 }}} ?
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First of all, we have to get rid of the fractions
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We have to find a common denominator with the fractions
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The first fraction, {{{ x/2 }}}, has "2" as its denominator
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The second fraction, {{{ x/3 }}}, has "3" as its denominator
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To find the common denominator, we would just multiply the two denominators together ( since there is no lower denominator we could use )
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{{{ 2(3) }}} = {{{ 6 }}}
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"6" is the common denominator, now if we multiply the two sides of the equation, it will get rid of the fractions, since they both will cancel out
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{{{ x/2+20=15+x/3 }}} = {{{ 6(x/2+20)=6(15+x/3) }}}
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We can now use the distributive property,
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{{{ highlight(6)(highlight(x/2)+20)=highlight(6)(highlight(15)+x/3) }}} = {{{ highlight(6)(x/2+highlight(20))=highlight(6)(15+highlight(x/3)) }}} = {{{ 6(x/2)+ 6(20)=6(15)+ 6(x/3) }}}
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{{{ 6(x/2)+ 6(20)=6(15)+ 6(x/3) }}} = {{{ 6x/2+ 120 = 90 + 6x/3 }}}, now we will simplify even further by dividing
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{{{ 6x/2+ 120 = 90 + 6x/3 }}} = {{{ (2(3x))/2+ 120 = 90 + (3(2x))/3 }}} = {{{ (highlight(2)(3x))/highlight(2)+ 120 = 90 + (highlight(3)(2x))/highlight(3) }}} = {{{ (cross(2)(3x))/cross(2)+ 120 = 90 + (cross(3)(2x))/cross(3) }}} = {{{ 3x + 120 = 90 + 2x }}}
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Now all we do is solve for "x", we will move "2x" to the left side
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{{{ 3x + 120 = 90 + 2x }}} = {{{ 3x - 2x + 120 = 90 + 2x - 2x }}} = {{{ x + 120 = 90 }}}, now we will move "120" to the right side
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{{{ x + 120 = 90 }}} = {{{ x + 120 - 120 = 90 - 120 }}} = {{{ x = (-30) }}}
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{{{ x = (-30) }}}
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You can check by replacing "x" with (-30) in the very original equation
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replace "x" with (-30), {{{ x/2+20=15+x/3 }}} = {{{ (-30)/2+20=15+(-30)/3 }}} = {{{ (-15)+20=15 - 30/3 }}} = {{{ (-15)+20=15 - 10 }}} = {{{ 5 = 5 }}} ( True )
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You have to be careful with fraction equations, because the denominator of a fraction cannot equal 0, so if one of the answers make a denominator 0, then that answer cannot work
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We don't have anything to worry about, since there are no "x"'s in the denominator
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{{{ x = (-30) }}}
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Hope I helped, Levi