Sure, let's go through each equation step-by-step:
### a) [tex]\( 8 + y = 25 \)[/tex]
To find [tex]\( y \)[/tex]:
1. Subtract 8 from both sides of the equation.
[tex]\[ y = 25 - 8 \][/tex]
[tex]\[ y = 17 \][/tex]
### b) [tex]\( 2x = 82 \)[/tex]
To find [tex]\( x \)[/tex]:
1. Divide both sides of the equation by 2.
[tex]\[ x = \frac{82}{2} \][/tex]
[tex]\[ x = 41 \][/tex]
### c) [tex]\( 3m = -48 \)[/tex]
To find [tex]\( m \)[/tex]:
1. Divide both sides of the equation by 3.
[tex]\[ m = \frac{-48}{3} \][/tex]
[tex]\[ m = -16 \][/tex]
### d) [tex]\( \frac{x}{2} = 15 \)[/tex]
To find [tex]\( x \)[/tex]:
1. Multiply both sides of the equation by 2.
[tex]\[ x = 15 \times 2 \][/tex]
[tex]\[ x = 30 \][/tex]
### e) [tex]\( 27 + p = 43 \)[/tex]
To find [tex]\( p \)[/tex]:
1. Subtract 27 from both sides of the equation.
[tex]\[ p = 43 - 27 \][/tex]
[tex]\[ p = 16 \][/tex]
### f) [tex]\( n^2 = 25 \)[/tex]
To find [tex]\( n \)[/tex]:
1. Take the square root of both sides. Consider both the positive and negative roots.
[tex]\[ n = \pm \sqrt{25} \][/tex]
[tex]\[ n = \pm 5 \][/tex]
So, [tex]\( n \)[/tex] can be [tex]\( 5 \)[/tex] or [tex]\( -5 \)[/tex].
### g) [tex]\( -\sqrt[3]{x} = -2 \)[/tex]
To find [tex]\( x \)[/tex]:
1. Multiply both sides by -1.
[tex]\[ \sqrt[3]{x} = 2 \][/tex]
2. Cube both sides of the equation.
[tex]\[ x = 2^3 \][/tex]
[tex]\[ x = 8 \][/tex]
Since the original equation had a negative sign before the cube root, we should negate the result:
[tex]\[ x = -8 \][/tex]
So the solutions to the equations are:
a) [tex]\( y = 17 \)[/tex]
b) [tex]\( x = 41 \)[/tex]
c) [tex]\( m = -16 \)[/tex]
d) [tex]\( x = 30 \)[/tex]
e) [tex]\( p = 16 \)[/tex]
f) [tex]\( n = 5 \)[/tex] and [tex]\( n = -5 \)[/tex]
g) [tex]\( x = -8 \)[/tex]
