4(x+ 2) ≥2x-2 find the range of x

To find the range of x that satisfies the inequality 4(x + 2) ≥ 2x - 2, we can solve it step by step. Let's begin: 4(x + 2) ≥ 2x - 2 First, distribute 4 to both terms inside the parentheses: 4x + 8 ≥ 2x - 2 Next, let's isolate the terms with x on one side of the inequality by subtracting 2x from both sides: 4x - 2x + 8 ≥ -2 Simplifying the left side: 2x + 8 ≥ -2 Now, let's isolate the term with x by subtracting 8 from both sides: 2x + 8 - 8 ≥ -2 - 8 Simplifying both sides: 2x ≥ -10 Finally, to solve for x, we divide both sides by 2. Since we are dividing by a positive number, the direction of the inequality remains the same: (2x)/2 ≥ (-10)/2 x ≥ -5 Therefore, the range of x that satisfies the inequality 4(x + 2) ≥ 2x - 2 is x ≥ -5.