Question

For this assignment, you will write and solve two different equations that meet the given requirements.

For full credit you must:

1. Create the equation based on the description/requirements.

2. Show all work to find the solution.

An example equation is provided. You will not receive credit for this practice if you copy the example equation to use as your own.



Create each type of equation, then show or explain how to solve it.

Answer 1

I don’t see the specific “given requirements” you mentioned, so I’ll provide two different original equations of common types and show complete work for solving each. If your assignment required particular types (e.g., linear, quadratic, absolute value, rational), tell me and I’ll adjust.

Equation 1 — two-step linear equation
Create: 3(x + 4) − 5 = 16

Solve:
1. Distribute: 3x + 12 − 5 = 16
2. Simplify constant terms: 3x + 7 = 16
3. Subtract 7 from both sides: 3x = 9
4. Divide both sides by 3: x = 3

Check: Substitute x = 3 into the original equation:
3(3 + 4) − 5 = 3(7) − 5 = 21 − 5 = 16 ✓

Solution: x = 3

Equation 2 — quadratic equation (solve by factoring)
Create: x^2 − 5x + 6 = 0

Solve:
1. Look for two numbers that multiply to +6 and add to −5: −2 and −3.
2. Factor: x^2 − 5x + 6 = (x − 2)(x − 3) = 0
3. Set each factor to zero:
x − 2 = 0 → x = 2
x − 3 = 0 → x = 3

Check: Substitute x = 2 and x = 3 into the original equation:
- For x = 2: 2^2 − 5(2) + 6 = 4 − 10 + 6 = 0 ✓
- For x = 3: 3^2 − 5(3) + 6 = 9 − 15 + 6 = 0 ✓

Solutions: x = 2 and x = 3

If you need different types (e.g., an absolute-value equation and a rational equation), or if your assignment had particular constraints, tell me and I’ll write and solve two equations meeting those requirements.