Question

business guru homework
solve each equation.

1. $1 + r = 2 + r$
2. $-8n + 8n = -5 - 7n + 8n$
3. $-8p + 8p = -16 - 2p$
4. $-4n - 7n = 15 + 1 - n - 8n$
5. $8x + 3x = 8x - 5 + 2x + 13$
6. $-7r - 6 + 6 = -2r - 5r$
7. $2n + 7 + 5 + 9 = 1 - 3n$
8. $m - 1 = -13 + 5m - 6m$
9. $2r + r = 3r - 2$
10. $0 = 3v - 3v$

Explanation:

1) Step1: Cancel $r$ from both sides

$1 = 2$

1) Step2: Evaluate validity

This is a false statement, so no solution exists.

2) Step1: Simplify like terms on both sides

$0 = -5 + n$

2) Step2: Isolate $n$

$n = 5$

3) Step1: Simplify left side terms

$0 = -16 - 2p$

3) Step2: Isolate $p$

$2p = -16$
$p = -8$

4) Step1: Combine like terms on both sides

$-11n = 16 - 9n$

4) Step2: Isolate $n$

$-11n + 9n = 16$
$-2n = 16$
$n = -8$

5) Step1: Combine like terms on both sides

$11x = 10x + 8$

5) Step2: Isolate $x$

$11x - 10x = 8$
$x = 8$

6) Step1: Simplify like terms on both sides

$-7r = -7r$

6) Step2: Evaluate validity

This is true for all real $r$, so infinitely many solutions exist.

7) Step1: Combine constants on left

$2n + 21 = 1 - 3n$

7) Step2: Isolate $n$

$2n + 3n = 1 - 21$
$5n = -20$
$n = -4$

8) Step1: Combine like terms on right

$m - 1 = -13 - m$

8) Step2: Isolate $m$

$m + m = -13 + 1$
$2m = -12$
$m = -6$

9) Step1: Combine like terms on left

$3r = 3r - 2$

9) Step2: Cancel $3r$ from both sides

$0 = -2$
This is a false statement, so no solution exists.

10) Step1: Simplify right side terms

$0 = 0$

10) Step2: Evaluate validity

This is true for all real $v$, so infinitely many solutions exist.

Answer:

1. No solution
2. $n=5$
3. $p=-8$
4. $n=-8$
5. $x=8$
6. Infinitely many solutions
7. $n=-4$
8. $m=-6$
9. No solution
10. Infinitely many solutions