Question

For #1-6, solve each equation and show your algebraic manipulations. Models are OPTIONAL. Model Algebraic Steps:

9 = 15 + 2p
-7 = 2h - 3
6 = 1 - 2n + 5
8x – 2 – 7x = –9
2(n – 5) = –4
-3(g – 3) = 6

Answer 1

To solve the equations:

1. Subtract 15 from 9, then divide by 2 to find p = -3
2. Add 3 to -7, then divide by 2 to find h = -2
3. Combine like terms, then divide by -2 to find n = 0
4. Combine like terms, then isolate the variable to find x = -7
5. Distribute and combine like terms, then isolate the variable to find n = 3
6. Distribute and combine like terms, then isolate the variable to find g = 1

Step-by-step explanation:

1. For the equation 9 = 15 + 2p, subtract 15 from both sides to isolate the variable, resulting in 2p = -6. Then, divide both sides by 2 to solve for p, giving you p = -3.
2. For the equation -7 = 2h - 3, add 3 to both sides to isolate the variable, resulting in 2h = -4. Then, divide both sides by 2 to solve for h, giving you h = -2.
3. For the equation 6 = 1 - 2n + 5, combine like terms to simplify, resulting in -2n = 0. Then, divide both sides by -2 to solve for n, giving you n = 0.
4. For the equation 8x - 2 - 7x = -9, combine like terms to simplify, resulting in x - 2 = -9. Then, add 2 to both sides to isolate the variable, resulting in x = -7.
5. For the equation 2(n - 5) = -4, distribute the 2 to both terms inside the parentheses, resulting in 2n - 10 = -4. Then, add 10 to both sides to isolate the variable, resulting in 2n = 6. Finally, divide both sides by 2 to solve for n, giving you n = 3.
6. For the equation -3(g - 3) = 6, distribute the -3 to both terms inside the parentheses, resulting in -3g + 9 = 6. Then, subtract 9 from both sides to isolate the variable, resulting in -3g = -3. Finally, divide both sides by -3 to solve for g, giving you g = 1.