find the solution set to this inequality: $2x - 3 > \\frac{2x - 5}{2}$\n$\\bigcirc x < \\frac{1}{2}$\n$\\bigc…

find the solution set to this inequality: $2x - 3 > \\frac{2x - 5}{2}$\n$\\bigcirc x < \\frac{1}{2}$\n$\\bigcirc x > \\frac{1}{2}$\n$\\bigcirc x \\leq \\frac{1}{2}$\n$\\bigcirc x \\geq \\frac{1}{2}$

find the solution set to this inequality: $2x - 3 > \\frac{2x - 5}{2}$\n$\\bigcirc x < \\frac{1}{2}$\n$\\bigcirc x > \\frac{1}{2}$\n$\\bigcirc x \\leq \\frac{1}{2}$\n$\\bigcirc x \\geq \\frac{1}{2}$

Answer

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the inequality (2x - 3>\frac{2x - 5}{2}) by (2) to get (2(2x - 3)>2x - 5). Using the distributive property (a(b + c)=ab+ac), we have (4x-6 > 2x - 5).

Step2: Move the terms with (x) to one side

Subtract (2x) from both sides: (4x-2x-6>2x - 2x- 5), which simplifies to (2x-6>-5).

Step3: Isolate the variable (x)

Add (6) to both sides: (2x-6 + 6>-5 + 6), so (2x>1). Divide both sides by (2): (x>\frac{1}{2}).

Answer:

(x > \frac{1}{2}) (corresponding to the option (x>\frac{1}{2}))