Answer :
Certainly! Let's solve each equation step-by-step.
### a) [tex]\( 8 + y = 25 \)[/tex]
To find the value of [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation:
1. Start with the equation:
[tex]\[ 8 + y = 25 \][/tex]
2. Subtract 8 from both sides:
[tex]\[ y = 25 - 8 \][/tex]
3. Simplify:
[tex]\[ y = 17 \][/tex]
So, the solution for [tex]\( y \)[/tex] is [tex]\( y = 17 \)[/tex].
### b) [tex]\( 2x = 82 \)[/tex]
To find the value of [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation by dividing both sides by 2:
1. Start with the equation:
[tex]\[ 2x = 82 \][/tex]
2. Divide both sides by 2:
[tex]\[ x = \frac{82}{2} \][/tex]
3. Simplify:
[tex]\[ x = 41 \][/tex]
So, the solution for [tex]\( x \)[/tex] is [tex]\( x = 41 \)[/tex].
### c) [tex]\( 3m = -48 \)[/tex]
To find the value of [tex]\( m \)[/tex], we need to isolate [tex]\( m \)[/tex] on one side of the equation by dividing both sides by 3:
1. Start with the equation:
[tex]\[ 3m = -48 \][/tex]
2. Divide both sides by 3:
[tex]\[ m = \frac{-48}{3} \][/tex]
3. Simplify:
[tex]\[ m = -16 \][/tex]
So, the solution for [tex]\( m \)[/tex] is [tex]\( m = -16 \)[/tex].
### d) [tex]\( \frac{x}{2} = 15 \)[/tex]
To find the value of [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation by multiplying both sides by 2:
1. Start with the equation:
[tex]\[ \frac{x}{2} = 15 \][/tex]
2. Multiply both sides by 2:
[tex]\[ x = 15 \times 2 \][/tex]
3. Simplify:
[tex]\[ x = 30 \][/tex]
So, the solution for [tex]\( x \)[/tex] is [tex]\( x = 30 \)[/tex].
### e) [tex]\( 27 + p = 43 \)[/tex]
To find the value of [tex]\( p \)[/tex], we need to isolate [tex]\( p \)[/tex] on one side of the equation:
1. Start with the equation:
[tex]\[ 27 + p = 43 \][/tex]
2. Subtract 27 from both sides:
[tex]\[ p = 43 - 27 \][/tex]
3. Simplify:
[tex]\[ p = 16 \][/tex]
So, the solution for [tex]\( p \)[/tex] is [tex]\( p = 16 \)[/tex].
### g) [tex]\( -\sqrt[3]{x} = -2 \)[/tex]
To find the value of [tex]\( x \)[/tex], we need to cube both sides of the equation to eliminate the cube root and then handle the negative sign:
1. Start with the equation:
[tex]\[ -\sqrt[3]{x} = -2 \][/tex]
2. Multiply both sides by -1 to get rid of the negative sign:
[tex]\[ \sqrt[3]{x} = 2 \][/tex]
3. Cube both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = 2^3 \][/tex]
4. Simplify:
[tex]\[ x = 8 \][/tex]
So, the solution for [tex]\( x \)[/tex] is [tex]\( x = -8 \)[/tex] (note the original sign considerations).
### ff) [tex]\( n^2 = 25 \)[/tex]
To find the value of [tex]\( n \)[/tex], we need to take the square root of both sides of the equation:
1. Start with the equation:
[tex]\[ n^2 = 25 \][/tex]
2. Take the square root of both sides:
[tex]\[ n = \sqrt{25} \][/tex]
3. Remember that the square root function has two solutions:
[tex]\[ n = \pm 5 \][/tex]
So, the solutions for [tex]\( n \)[/tex] are [tex]\( n = 5 \)[/tex] and [tex]\( n = -5 \)[/tex].
However, typically the principal square root is positive unless context states otherwise, so we have:
[tex]\( n = 5 \)[/tex].
### Summary of Solutions
- 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]
- g) [tex]\( x = -8 \)[/tex]
- ff) [tex]\( n = 5 \)[/tex]
### a) [tex]\( 8 + y = 25 \)[/tex]
To find the value of [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation:
1. Start with the equation:
[tex]\[ 8 + y = 25 \][/tex]
2. Subtract 8 from both sides:
[tex]\[ y = 25 - 8 \][/tex]
3. Simplify:
[tex]\[ y = 17 \][/tex]
So, the solution for [tex]\( y \)[/tex] is [tex]\( y = 17 \)[/tex].
### b) [tex]\( 2x = 82 \)[/tex]
To find the value of [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation by dividing both sides by 2:
1. Start with the equation:
[tex]\[ 2x = 82 \][/tex]
2. Divide both sides by 2:
[tex]\[ x = \frac{82}{2} \][/tex]
3. Simplify:
[tex]\[ x = 41 \][/tex]
So, the solution for [tex]\( x \)[/tex] is [tex]\( x = 41 \)[/tex].
### c) [tex]\( 3m = -48 \)[/tex]
To find the value of [tex]\( m \)[/tex], we need to isolate [tex]\( m \)[/tex] on one side of the equation by dividing both sides by 3:
1. Start with the equation:
[tex]\[ 3m = -48 \][/tex]
2. Divide both sides by 3:
[tex]\[ m = \frac{-48}{3} \][/tex]
3. Simplify:
[tex]\[ m = -16 \][/tex]
So, the solution for [tex]\( m \)[/tex] is [tex]\( m = -16 \)[/tex].
### d) [tex]\( \frac{x}{2} = 15 \)[/tex]
To find the value of [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation by multiplying both sides by 2:
1. Start with the equation:
[tex]\[ \frac{x}{2} = 15 \][/tex]
2. Multiply both sides by 2:
[tex]\[ x = 15 \times 2 \][/tex]
3. Simplify:
[tex]\[ x = 30 \][/tex]
So, the solution for [tex]\( x \)[/tex] is [tex]\( x = 30 \)[/tex].
### e) [tex]\( 27 + p = 43 \)[/tex]
To find the value of [tex]\( p \)[/tex], we need to isolate [tex]\( p \)[/tex] on one side of the equation:
1. Start with the equation:
[tex]\[ 27 + p = 43 \][/tex]
2. Subtract 27 from both sides:
[tex]\[ p = 43 - 27 \][/tex]
3. Simplify:
[tex]\[ p = 16 \][/tex]
So, the solution for [tex]\( p \)[/tex] is [tex]\( p = 16 \)[/tex].
### g) [tex]\( -\sqrt[3]{x} = -2 \)[/tex]
To find the value of [tex]\( x \)[/tex], we need to cube both sides of the equation to eliminate the cube root and then handle the negative sign:
1. Start with the equation:
[tex]\[ -\sqrt[3]{x} = -2 \][/tex]
2. Multiply both sides by -1 to get rid of the negative sign:
[tex]\[ \sqrt[3]{x} = 2 \][/tex]
3. Cube both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = 2^3 \][/tex]
4. Simplify:
[tex]\[ x = 8 \][/tex]
So, the solution for [tex]\( x \)[/tex] is [tex]\( x = -8 \)[/tex] (note the original sign considerations).
### ff) [tex]\( n^2 = 25 \)[/tex]
To find the value of [tex]\( n \)[/tex], we need to take the square root of both sides of the equation:
1. Start with the equation:
[tex]\[ n^2 = 25 \][/tex]
2. Take the square root of both sides:
[tex]\[ n = \sqrt{25} \][/tex]
3. Remember that the square root function has two solutions:
[tex]\[ n = \pm 5 \][/tex]
So, the solutions for [tex]\( n \)[/tex] are [tex]\( n = 5 \)[/tex] and [tex]\( n = -5 \)[/tex].
However, typically the principal square root is positive unless context states otherwise, so we have:
[tex]\( n = 5 \)[/tex].
### Summary of Solutions
- 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]
- g) [tex]\( x = -8 \)[/tex]
- ff) [tex]\( n = 5 \)[/tex]
