Question

Please help with math problem !! (explanation needed) -3 + (8 – 2x)4 = 29

Answer 1

x = -4

Explanation:

To solve this type of question, put the term with the exponent on one side and the numerical term on the other side

∵ -3 +
`(8-2x)^{(5)/(4)}` = 29

→ Add 3 to both sides

∵ -3 + 3 +
`(8-2x)^{(5)/(4)}` = 29 + 3

∴
`(8-2x)^{(5)/(4)}` = 32

→ Remember is
`x^{(m)/(n)}` = a, then x =
`a^{(n)/(m)}`, that means to move the exponent

from one side to the other side reciprocal it

∴ 8 - 2x =
`(32)^{(4)/(5)}`

→ Use your calculator to find the value of
`(32)^{(4)/(5)}`

∵
`(32)^{(4)/(5)}` = 16

∴ 8 - 2x = 16

→ Subtract 8 from both sides

∴ 8 - 8 - 2x = 16 - 8

∴ -2x = 8

→ Divide both sides by -2

∴ x = -4

To check the solution substitute x by -4 in the left side and find its answer if it equals the right side, then the solution is right

∵ Left side ⇒ -3 + (8 - 2 × -4)
`^{(5)/(4)}` = -3 + (8 + 8)
`^{(5)/(4)}` =-3 + (16)
`^{(5)/(4)}` = -3 + 32 = 29

∵ Right side = 29

∴ The solution is right