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.

Equation 1: All terms are decimals

Equation 2: The distributive property is used and the coefficient to the variable is a fraction.

Answer 1

Here are two different equations that meet the requirements, with all steps shown.

Equation 1 — All terms are decimals
Equation: 0.5x + 1.25 = 3.75

Solve:
1. Subtract 1.25 from both sides:
0.5x + 1.25 − 1.25 = 3.75 − 1.25
0.5x = 2.50
2. Divide both sides by 0.5:
x = 2.50 ÷ 0.5 = 5

Check:
0.5(5) + 1.25 = 2.50 + 1.25 = 3.75 ✔

Equation 2 — Uses distributive property and the coefficient of the variable is a fraction
Equation: (1/4)(x + 8) = 5

Solve:
1. Use the distributive property: (1/4)(x) + (1/4)(8) = 5
(1/4)x + 2 = 5
2. Subtract 2 from both sides:
(1/4)x = 3
3. Multiply both sides by 4 to isolate x:
x = 3 × 4 = 12

Check:
(1/4)(12 + 8) = (1/4)(20) = 5 ✔

Answers: Equation 1 gives x = 5. Equation 2 gives x = 12.