Question

5/8 (x + 1/2) = 100

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for x in the equation 5/8 (x + 1/2) = 100, we need to follow a step-by-step process.

1. Distribute the 5/8 to the terms inside the parentheses:
(5/8) * x + (5/8) * (1/2) = 100

This simplifies to: 5/8 * x + 5/16 = 100

2. Multiply the denominators to get a common denominator:
Multiply 8 and 16 = 128

The equation becomes: (5/8) * x + (5/16) * x = 100

3. Multiply each term by the common denominator (128) to eliminate fractions:
128 * (5/8) * x + 128 * (5/16) * x = 128 * 100

Simplify to: 16 * 5x + 8 * 5x = 12800

4. Combine like terms on both sides of the equation:
80x + 40x = 12800

Simplify to: 120x = 12800

5. Divide both sides of the equation by 120 to solve for x:
x = 12800 / 120

Simplify to: x = 106.67

Therefore, the solution to the equation 5/8 (x + 1/2) = 100 is x = 106.67.

Answer 2

[AI-generated answer — Explain Bot]

To solve the equation 5/8 (x + 1/2) = 100, you can follow these steps:

Step 1: Simplify the equation by distributing the fraction 5/8 to the terms inside the parentheses:
(x + 1/2) * 5/8 = 100

Step 2: Multiply the numerators (x + 1/2) and 5 together:
5(x + 1/2)/8 = 100

Step 3: Distribute the numerator 5 to each term inside the parentheses:
(5x + 5/2)/8 = 100

Step 4: Multiply both sides of the equation by 8 to eliminate the fraction in the denominator:
8 * (5x + 5/2)/8 = 100 * 8

Simplifying:
5x + 5/2 = 800

Step 5: Subtract 5/2 from both sides of the equation:
5x + 5/2 - 5/2 = 800 - 5/2

Simplifying:
5x = 800 - 5/2

Step 6: Simplify the right side of the equation:
5x = 797.5

Step 7: Divide both sides of the equation by 5 to solve for x:
5x/5 = 797.5/5

Simplifying:
x = 159.5

Therefore, the solution to the equation 5/8 (x + 1/2) = 100 is x = 159.5.