Question

Solve the following equation for w
3w-7= √8w-7

Answer 1

Explanation:

to
`3w - 7 = √(8w - 7) \\ {(3w - 7)}^(2) = ({ √(8w - 7) })^(2) \\ 9 {w}^(2) - 42w + 49 = 8w - 7 \\ 9 { w}^(2) - 42w - 8w + 49 + 7 = 0 \\ 9 {w}^(2) - 50w + 56 = 0 \\ (9w - 14)(w - 4) = 0 \\ w = (14)/(9) \: or \: w = 4`

to make sure the answer

substitute w = 14/9 and w = 4 to the equation.

if w = 14/9

`3w - 7 = √(8 w - 7) \\ 3 * (14)/(9) - 7 = \sqrt{8 * (14)/(9) - 7} \\ - ( 7)/(3) = (7)/(3)`

we know that if we substitute w = 14/9, the answer is not the same.

if w = 4

`3w - 7 = √( 8 w - 7 ) \\ 3 * 4 - 7 = √(8 * 4 - 7) \\ 5 = 5`

if we substitute w = 4 the answer is the same.. we can conclude the the answer of 3w - 7 = √8w - 4 is 4

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