Question

Solve for the unknown variable in each equation using an algebraic method(undoing or rewriting)

I need to know how to do it, not the answer, just need to learn how to do it show work and steps please

Answer 1

a. x=2√3+3 and x = - 2√3 +3

b. x=29.5

c. x=2/3, x= - 2

d. x=25

Explanation:

a). -2(x-3)² +5 = - 19

- 2(x-3)² = -19 - 5

- 2(x-3)² = - 24

(x-3)² = 12

x-3 = √12 and x-3 = -√12

x-3 =2√3 and x-3= -2√3

x=2√3+3 and x = - 2√3 +3

b)

`(√(2x+5) )/(4) +1=3\\\\\\(√(2x+5) )/(4) =2\\√(2x+5) =8\\\\(√(2x+5) )^(2)=8^(2)\\2x+5=64\\2x= 59\\x=29.5`

c)

-5|3x+2| - 4 = -24

-5|3x + 2| = - 20

|3x +2| = 4

3x+2=4 or - (3x+2)=4

3x=2 or 3x+2 = - 4

x=2/3 or 3x = - 6, x= -2

d)

`5\sqrt[3]{x+2} -7=8\\\\5\sqrt[3]{x+2} =15\\\\\sqrt[3]{x+2} =3\\x+2 = 3^(3)\\x+2=27\\x=25`