Answer:
x = -4
Step-by-step 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 + [tex](8-2x)^{\frac{5}{4}}[/tex] = 29
→ Add 3 to both sides
∵ -3 + 3 + [tex](8-2x)^{\frac{5}{4}}[/tex] = 29 + 3
∴ [tex](8-2x)^{\frac{5}{4}}[/tex] = 32
→ Remember is [tex]x^{\frac{m}{n}}[/tex] = a, then x = [tex]a^{\frac{n}{m}}[/tex], that means to move the exponent
from one side to the other side reciprocal it
∴ 8 - 2x = [tex](32)^{\frac{4}{5}}[/tex]
→ Use your calculator to find the value of [tex](32)^{\frac{4}{5}}[/tex]
∵ [tex](32)^{\frac{4}{5}}[/tex] = 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)[tex]^{\frac{5}{4}}[/tex] = -3 + (8 + 8)[tex]^{\frac{5}{4}}[/tex] =-3 + (16)[tex]^{\frac{5}{4}}[/tex] = -3 + 32 = 29
∵ Right side = 29
∴ The solution is right
