Solve the inequality below. Give the solution using interval notation. Give all values as integers or reduced fractions. (Do not convert fractions to decimals.) $$ 4(x-2) \geq 2 x-4 $$

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UpStudy AI · Accepted Answer

To solve the inequality $$ 4(x - 2) \geq 2x - 4 $$:

1. **Expand the left side:**
   $$
   4(x - 2) = 4x - 8
   $$
   So the inequality becomes:
   $$
   4x - 8 \geq 2x - 4
   $$

2. **Move all $$ x $$-terms to one side and constants to the other:**
   $$
   4x - 2x \geq -4 + 8
   $$
   Simplifying:
   $$
   2x \geq 4
   $$

3. **Divide both sides by 2:**
   $$
   x \geq 2
   $$

**Solution in interval notation:**
$$
[2, \infty)
$$

**Final Answer:**

$$\boxed{\, [2,\ \infty) \,}$$
The solution is $$ x \geq 2 $$, which in interval notation is $$[2, \infty)$$.

Solve the inequality below. Give the solution using interval notation. Give all values as integers or reduced fractions. (Do not convert fractions to decimals.) \( 4(x-2) \geq 2 x-4 \)

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