25.
[tex]b = \frac{2}{10} = \frac{1}{5} \\ [/tex]
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26 .
[tex]c = \frac{5}{6} \\ [/tex]
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27 .
[tex]d = \frac{6}{6} = 1 \\ [/tex]
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31 .
[tex]x - 3 = \sqrt{ {x}^{2} - 6x + 9} [/tex]
[tex]x - 3 = \sqrt{ ({x - 3})^{2} } [/tex]
[tex]x - 3 = |x - 3| [/tex]
Thus :
[tex]x - 3 = x - 3[/tex]
[tex]x = infinite \: solutions[/tex]
OR
[tex]x - 3 = - (x - 3)[/tex]
[tex]x - 3 = - x + 3[/tex]
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
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32.
[tex]10 = 2 \sqrt{3 - 2t} [/tex]
Divide both sides by 2
[tex] \frac{10}{2} = \frac{2 \sqrt{3 - 2t} }{2} \\ [/tex]
[tex]5 = \sqrt{3 - 2t} [/tex]
[tex] ({5})^{2} = ({ \sqrt{3 - 2t} })^{2} [/tex]
[tex]25 = |3 - 2t| [/tex]
Switch sides
[tex] |3 - 2t| = 25[/tex]
Thus :
[tex]3 - 2t = 25[/tex]
Subtract both sides 3
[tex]3 - 3 - 2t = 25 - 3[/tex]
[tex] - 2t = 22[/tex]
Divide both sides by -2
[tex] \frac{ - 2t}{ - 2} = \frac{22}{ - 2} \\ [/tex]
[tex]t = - 11 \: \: \: acceptable[/tex]
Or
[tex]3 - 2t = - 25[/tex]
Subtract both sides 3
[tex]3 - 3 - 2t = - 25 - 3[/tex]
[tex] - 2t = - 28[/tex]
Divide both sides by -2
[tex] \frac{ - 2t}{ - 2} = \frac{ - 28}{ - 2} \\ [/tex]
[tex]t = 14 \: \: \: unacceptable[/tex]
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33.
[tex]3 - ({2p - 4})^{ \frac{1}{3} } = 2 [/tex]
Subtract both sides 3
[tex]3 - 3 - \sqrt[3]{2p - 4} = 2 - 3[/tex]
[tex] - \sqrt[3]{2p - 4} = - 1[/tex]
[tex] \sqrt[3]{2p - 4} = 1[/tex]
[tex] ({ \sqrt[3]{2p - 4} })^{3} = ({1})^{3} [/tex]
[tex]2p - 4 = 1[/tex]
Add both sides 4
[tex]2p - 4 + 4 = 1 + 4[/tex]
[tex]2p = 5[/tex]
Divide both sides by 2
[tex] \frac{2p}{2} = \frac{5}{2} \\ [/tex]
[tex]p = \frac{5}{2} \\ [/tex]
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34.
[tex]r = \sqrt{ - 1 - 2r} [/tex]
[tex] ({r})^{2} = ({ \sqrt{ - 1 - 2r} })^{2} [/tex]
[tex] {r}^{2} = | - 1 - 2r| [/tex]
[tex] {r}^{2} = - 1 - 2r[/tex]
[tex] {r}^{2} + 2r + 1 = 0[/tex]
[tex] ({r + 1})^{2} = 0 [/tex]
[tex]r + 1 = 0[/tex]
[tex]r = - 1[/tex]
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35.
[tex] \sqrt{m + 2} = \sqrt{2m} [/tex]
[tex] ({ \sqrt{m + 2} })^{2} = ({ \sqrt{2m} })^{2} [/tex]
[tex] |m + 2| = |2m| [/tex]
Thus :
[tex]m + 2 = 2m[/tex]
Switch sides
[tex]2m = m + 2[/tex]
Subtract both sides m
[tex]2m - m = m - m + 2[/tex]
[tex]m = 2 \: \: acceptable[/tex]
Or
[tex]2m = - (m + 2)[/tex]
[tex]2m = - m - 2[/tex]
Add both sides m
[tex]2m + m = - m + m - 2[/tex]
[tex]3m = - 2[/tex]
Divide both sides by 3
[tex] \frac{3m}{3} = \frac{ - 2}{3} \\ [/tex]
[tex]m = - \frac{2}{3} \: \: unacceptable \\ [/tex]
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36 .
[tex] \sqrt[3]{4x + 1} - \sqrt[3]{6x - 9} = 0[/tex]
[tex] \sqrt[3]{4x + 1} = \sqrt[3]{6x - 9} [/tex]
[tex] ({ \sqrt[3]{4x + 1} })^{3} = ({ \sqrt[3]{6x - 9} })^{3} [/tex]
[tex]4x + 1 = 6x - 9[/tex]
Switch sides
[tex]6x - 9 = 4x + 1[/tex]
Subtract both sides 4x
[tex]6x - 4x - 9 = 4x - 4x + 1[/tex]
[tex]2x - 9 = 1[/tex]
Add both sides 9
[tex]2x - 9 + 9 = 1 + 9[/tex]
[tex]2x = 10[/tex]
Divide both sides by 2
[tex] \frac{2x}{2} = \frac{10}{2} \\ [/tex]
[tex]x = 5[/tex]
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The last one is yours bro you got this ....
Have a great time ♡♡
