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# Solving functions.

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How do you solve these? For some reason the answers I get with these look so wrong to me.

Jun 7, 2019

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 a.__ -4x6  =  -2916 ___ Divide both sides of the equation by  -4 x6  =  729 Take the ± 6th root of both sides x  =  $$\pm\sqrt[6]{729}$$ Plug this into a calculator or note that  36  =  729  so we can rewrite  729  as  36 x  =  $$\pm\sqrt[6]{3^6}$$ Simplify x  =  ± 3 This equation has two solutions. There are two values of  x  which make the equation true. They are:  x = 3   and   x = -3 b. 93 - 7x3  =  23 Subtract  93  from both sides of the equation. -7x3  =  -70 Divide both sides of the equation by  -7 x3  =  10 Take the cube root of both sides. x  =  $$\sqrt[3]{10}$$ To get an approximate solution, plug  $$\sqrt[3]{10}$$  into a calculator. x  ≈  2.154 c. (-5p)5  =  -65 Take the fifth root of both sides. -5p  =  $$\sqrt[5]{-65}$$ Divide both sides by  -5 p  =  $$\frac{\sqrt[5]{-65}}{-5}$$ SImplify p  =  $$\frac{\sqrt[5]{-1}\,\cdot\,\sqrt[5]{65}}{-5}$$ p  =  $$\frac{-1\ \cdot\ \sqrt[5]{65}}{-5}$$ p  =  $$\frac{\sqrt[5]{65}}{5}$$ p  ≈  0.461 d. $$-7+\frac{14}{x-3}\ =\ -5$$ Add  7  to both sides. $$\frac{14}{x-3}\ =\ 2$$ Multiply both sides by  (x - 3)  and note  x ≠ 3 14  =  2(x - 3) Divide both sides by  2 7  =  x - 3 Add  3  to both sides 10  =  x x  =  10
Jun 7, 2019

 a.__ -4x6  =  -2916 ___ Divide both sides of the equation by  -4 x6  =  729 Take the ± 6th root of both sides x  =  $$\pm\sqrt[6]{729}$$ Plug this into a calculator or note that  36  =  729  so we can rewrite  729  as  36 x  =  $$\pm\sqrt[6]{3^6}$$ Simplify x  =  ± 3 This equation has two solutions. There are two values of  x  which make the equation true. They are:  x = 3   and   x = -3 b. 93 - 7x3  =  23 Subtract  93  from both sides of the equation. -7x3  =  -70 Divide both sides of the equation by  -7 x3  =  10 Take the cube root of both sides. x  =  $$\sqrt[3]{10}$$ To get an approximate solution, plug  $$\sqrt[3]{10}$$  into a calculator. x  ≈  2.154 c. (-5p)5  =  -65 Take the fifth root of both sides. -5p  =  $$\sqrt[5]{-65}$$ Divide both sides by  -5 p  =  $$\frac{\sqrt[5]{-65}}{-5}$$ SImplify p  =  $$\frac{\sqrt[5]{-1}\,\cdot\,\sqrt[5]{65}}{-5}$$ p  =  $$\frac{-1\ \cdot\ \sqrt[5]{65}}{-5}$$ p  =  $$\frac{\sqrt[5]{65}}{5}$$ p  ≈  0.461 d. $$-7+\frac{14}{x-3}\ =\ -5$$ Add  7  to both sides. $$\frac{14}{x-3}\ =\ 2$$ Multiply both sides by  (x - 3)  and note  x ≠ 3 14  =  2(x - 3) Divide both sides by  2 7  =  x - 3 Add  3  to both sides 10  =  x x  =  10