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Change the Subject of an Equation>
Change the Subject of an Equation 1Change the Subject of an Equation 1
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Question 1 of 5
1. Question
Write `r` as the subject of the equation below`V=pir^2h`Hint
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equationDivide both sides of the equation by `pih``V` `=` `pir^2h` `V``-:pih` `=` `pir^2h``-:pih` `V/(pih)` `=` `r^2` `pih-:pih` cancels out Get the square root of both sides`V/(pih)` `=` `r^2` `sqrt(V/(pih))` `=` `sqrt(r^2)` `sqrt(V/(pih))` `=` `r` `r` `=` `sqrt(V/(pih))` Interchange the sides `r=sqrt(V/(pih))` -
Question 2 of 5
2. Question
Write `a` as the subject of the equation below`b=(a-3)/(a-4)`Hint
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equationMultiply both sides of the equation to `a-4``b` `=` `(a-3)/(a-4)` `b``xx(a-4)` `=` `(a-3)/(a-4)``xx(a-4)` `b(a-4)` `=` `a-3` `1/(a-4)xx(a-4)` cancels out `ab-4b` `=` `a-3` Leave only `a` terms on the left`ab-4b` `=` `a-3` `ab-4b` `-a` `=` `a-3` `-a` Subtract `a` from both sides `ab-4b-a` `=` `-3` `a-a` cancels out `ab-4b-a` `+4b` `=` `-3` `+4b` Add `4b` to both sides `ab-a` `=` `4b-3` `-4b+4b` cancels out Factor out `a``ab-a` `=` `4b-3` `a(b-1)` `=` `4b-3` Finally, divide both sides by `b-1``a(b-1)` `=` `4b-3` `a(b-1)``-:(b-1)` `=` `(4b-3)``-:(b-1)` `a` `=` `(4b-3)/(b-1)` `a=(4b-3)/(b-1)` -
Question 3 of 5
3. Question
Write `x` as the subject of the equation below`7-3x=mx+t`Hint
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equationKeep only `x` terms on the right side`7-3x` `=` `mx+t` `7-3x` `+3x` `=` `mx+t` `+3x` Add `3x` to both sides `7` `=` `mx+3x+t` `-3x+3x` cancels out `7` `-t` `=` `mx+3x+t` `-t` Subtract `t` from both sides `7-t` `=` `mx+3x` `t-t` cancels out Factor out `x``7-t` `=` `mx+3x` `7-t` `=` `x(m+3)` Finally, divide both sides by `m+3``7-t` `=` `x(m+3)` `(7-t)``-:(m+3)` `=` `x(m+3)``-:(m+3)` `(7-t)/(m+3)` `=` `x` `x` `=` `(7-t)/(m+3)` Interchange the sides `x=(7-t)/(m+3)` -
Question 4 of 5
4. Question
Write `x` as the subject of the equation below`(1-x)/(x+y)=1`Hint
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equationMultiply both sides to `x+y``(1-x)/(x+y)` `=` `1` `(1-x)/(x+y)``xx(x+y)` `=` `1``xx(x+y)` `1-x` `=` `x+y` `1/(x+y)xx(x+y)` cancels out Leave only the `x` terms on the right side`1-x` `=` `x+y` `1-x` `+x` `=` `x+y` `+x` Add `x` to both sides `1` `=` `2x+y` `-x+x` cancels out `1` `-y` `=` `2x+y` `-y` Subtract `y` from both sides `1-y` `=` `2x` `y-y` cancels out Finally, divide both sides by `2``1-y` `=` `2x` `(1-y)``-:2` `=` `2x``-:2` `(1-y)/2` `=` `x` `2-:2` cancels out `x` `=` `(1-y)/2` Interchange the sides `x=(1-y)/2` -
Question 5 of 5
5. Question
Write `b` as the subject of the equation below`x=(2b)/(3b+y)`Hint
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Changing the subject means operating on an equation so that a chosen variable remains alone on the left side of the equationMultiply both sides to `3b+y``x` `=` `(2b)/(3b+y)` `x``xx(3b+y)` `=` `(2b)/(3b+y)``xx(3b+y)` `x(3b+y)` `=` `2b` `1/(3b+y)xx(3b+y)` cancels out `3bx+xy` `=` `2b` Distribute `x` Leave only `b` terms on the left side`3bx+xy` `=` `2b` `3bx+xy` `-xy` `=` `2b` `-xy` Subtract `xy` from both sides `3bx` `=` `2b-xy` `xy-xy` cancels out `3bx` `-2b` `=` `2b-xy` `-2b` Subtract `2b` from both sides `3bx-2b` `=` `-xy` `2b-2b` cancels out Factor out `b``3bx-2b` `=` `-xy` `b(3x-2)` `=` `-xy` Finally, divide both sides by `3x-2``b(3x-2)` `=` `-xy` `b(3x-2)``-:(3x-2)` `=` `-xy``-:(3x-2)` `b` `=` `(-xy)/(3x-2)` `(3x-2)-:(3x-2)` cancels out `b=(-xy)/(3x-2)`
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