Question

Can someone please help its like really important and due today please!

Answer 1

25.

`b = (2)/(10) = (1)/(5) \\`

_____________________________________________

26 .

`c = (5)/(6) \\`

_____________________________________________

27 .

`d = (6)/(6) = 1 \\`

_____________________________________________

31 .

`x - 3 = \sqrt{ {x}^(2) - 6x + 9}`

`x - 3 = \sqrt{ ({x - 3})^(2) }`

`x - 3 = |x - 3|`

Thus :

`x - 3 = x - 3`

`x = infinite \: solutions`

OR

`x - 3 = - (x - 3)`

`x - 3 = - x + 3`

`2x = 6`

`x = 3`

_____________________________________________

32.

`10 = 2 √(3 - 2t)`

Divide both sides by 2

`(10)/(2) = (2 √(3 - 2t) )/(2) \\`

`5 = √(3 - 2t)`

`({5})^(2) = ({ √(3 - 2t) })^(2)`

`25 = |3 - 2t|`

Switch sides

`|3 - 2t| = 25`

Thus :

`3 - 2t = 25`

Subtract both sides 3

`3 - 3 - 2t = 25 - 3`

`- 2t = 22`

Divide both sides by -2

`( - 2t)/( - 2) = (22)/( - 2) \\`

`t = - 11 \: \: \: acceptable`

Or

`3 - 2t = - 25`

Subtract both sides 3

`3 - 3 - 2t = - 25 - 3`

`- 2t = - 28`

Divide both sides by -2

`( - 2t)/( - 2) = ( - 28)/( - 2) \\`

`t = 14 \: \: \: unacceptable`

_____________________________________________

33.

`3 - ({2p - 4})^{ (1)/(3) } = 2`

Subtract both sides 3

`3 - 3 - \sqrt[3]{2p - 4} = 2 - 3`

`- \sqrt[3]{2p - 4} = - 1`

`\sqrt[3]{2p - 4} = 1`

`({ \sqrt[3]{2p - 4} })^(3) = ({1})^(3)`

`2p - 4 = 1`

Add both sides 4

`2p - 4 + 4 = 1 + 4`

`2p = 5`

Divide both sides by 2

`(2p)/(2) = (5)/(2) \\`

`p = (5)/(2) \\`

_____________________________________________

34.

`r = √( - 1 - 2r)`

`({r})^(2) = ({ √( - 1 - 2r) })^(2)`

`{r}^(2) = | - 1 - 2r|`

`{r}^(2) = - 1 - 2r`

`{r}^(2) + 2r + 1 = 0`

`({r + 1})^(2) = 0`

`r + 1 = 0`

`r = - 1`

_____________________________________________

35.

`√(m + 2) = √(2m)`

`({ √(m + 2) })^(2) = ({ √(2m) })^(2)`

`|m + 2| = |2m|`

Thus :

`m + 2 = 2m`

Switch sides

`2m = m + 2`

Subtract both sides m

`2m - m = m - m + 2`

`m = 2 \: \: acceptable`

Or

`2m = - (m + 2)`

`2m = - m - 2`

Add both sides m

`2m + m = - m + m - 2`

`3m = - 2`

Divide both sides by 3

`(3m)/(3) = ( - 2)/(3) \\`

`m = - (2)/(3) \: \: unacceptable \\`

_____________________________________________

36 .

`\sqrt[3]{4x + 1} - \sqrt[3]{6x - 9} = 0`

`\sqrt[3]{4x + 1} = \sqrt[3]{6x - 9}`

`({ \sqrt[3]{4x + 1} })^(3) = ({ \sqrt[3]{6x - 9} })^(3)`

`4x + 1 = 6x - 9`

Switch sides

`6x - 9 = 4x + 1`

Subtract both sides 4x

`6x - 4x - 9 = 4x - 4x + 1`

`2x - 9 = 1`

Add both sides 9

`2x - 9 + 9 = 1 + 9`

`2x = 10`

Divide both sides by 2

`(2x)/(2) = (10)/(2) \\`

`x = 5`

_____________________________________________

The last one is yours bro you got this ....

Have a great time ♡♡