1. Multiplication property of equality: We can multiply both sides of an equation by the same number without changing the equality.
2. Addition property of equality: We can add the same number to both sides of an equation without changing the equality.
3. Distributive property: We can distribute a number to each term inside parentheses.
4. Transitive property: If a = b and b = c, then a = c.
5. Subtraction property of equality: We can subtract the same number from both sides of an equation without changing the equality.
6. Combining like terms: We can combine terms that have the same variable and exponent.
Steps:
1. Distribute -2 to (3-2): -2 * 3 + (-2) * (-2) = -6 + 4 = -2.
2. Simplify both sides: 3(z + 4) + 5 = 2z - 2 + (-2) = 3z + 12 + 5 = 3z + 17.
3. Distribute 2 to (3-2): 2 * 3z + 2 * (-2) = 6z - 4.
4. Simplify both sides: 3z + 17 = 6z - 4.
5. Subtract 3z from both sides: 3z + 17 - 3z = 6z - 4 - 3z.
6. Simplify both sides: 17 = 3z - 4.
7. Add 4 to both sides: 17 + 4 = 3z - 4 + 4.
8. Simplify both sides: 21 = 3z.
9. Divide both sides by 3: 21/3 = 3z/3.
10. Simplify both sides: 7 = z.
By following these steps and applying the mentioned properties, we can find that the solution to the equation is z = 7.
good luck !!