Question

(\frac{x - 10}{8} geq \frac{x - 5}{12} + \frac{1}{24})

Explanation:

Step1: Eliminate denominators (LCM=24)

Multiply all terms by 24:
$$24\times\frac{x-10}{8} \geq 24\times\frac{x-5}{12} + 24\times\frac{1}{24}$$
Simplify each term:
$$3(x-10) \geq 2(x-5) + 1$$

Step2: Expand parentheses

$$3x - 30 \geq 2x - 10 + 1$$

Step3: Simplify right-hand side

$$3x - 30 \geq 2x - 9$$

Step4: Isolate x term

Subtract $2x$ from both sides:
$$3x - 2x - 30 \geq -9$$
$$x - 30 \geq -9$$

Step5: Solve for x

Add 30 to both sides:
$$x \geq -9 + 30$$
$$x \geq 21$$

Answer:

$x \geq 21$