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