To solve the inequality \(-\left(28x + \frac{12}{8}\right) < 6x - 30\), we can start by simplifying the inequality.
First, simplify \(\frac{12}{8}\): \[ \frac{12}{8} = \frac{3}{2} \] So the inequality becomes: \[ -(28x + \frac{3}{2}) < 6x - 30 \] Next, distribute the negative sign: \[ -28x - \frac{3}{2} < 6x - 30 \] Now, we will add \(28x\) to both sides of the inequality: \[ -\frac{3}{2} < 6x + 28x - 30 \] This simplifies to: \[ -\frac{3}{2} < 34x - 30 \] Now, add \(30\) to both sides: \[ -\frac{3}{2} + 30 < 34x \] Convert \(30\) into a fraction with a denominator of 2: \[ 30 = \frac{60}{2} \] Thus, \[ -\frac{3}{2} + \frac{60}{2} < 34x \] Now combine the fractions: \[ \frac{57}{2} < 34x \] Next, divide both sides by \(34\): \[ \frac{57}{2 \cdot 34} < x \] Simplifying \(2 \cdot 34 = 68\): \[ \frac{57}{68} < x \] Which can be rewritten as: \[ x > \frac{57}{68} \]
Thus, the solution to the inequality is: \[ x > \frac{57}{68} \]