Question

solve the inequality.
\\(\frac{2x - 3}{4} + 6 < x + 1\\)
\\(x < -\frac{31}{2}\\) \\(x > 1\\) \\(x > \frac{17}{2}\\) \\(x > \frac{31}{2}\\)

Explanation:

Step1: Eliminate denominator

Multiply all terms by 4:
$$4\times\frac{2x-3}{4} + 4\times6 < 4\times(x+1)$$
Simplify to get:
$$2x - 3 + 24 < 4x + 4$$

Step2: Simplify both sides

Combine constant terms:
$$2x + 21 < 4x + 4$$

Step3: Isolate x terms

Subtract $2x$ from both sides:
$$21 < 2x + 4$$

Step4: Isolate constant terms

Subtract 4 from both sides:
$$17 < 2x$$

Step5: Solve for x

Divide by 2:
$$\frac{17}{2} < x$$
Rewrite as:
$$x > \frac{17}{2}$$

Answer:

$x > \frac{17}{2}$ (matches the third option)