Solve the inequality \( -8 x-10>7 x+20 \) \( x>-30 \) \( x>-2 \) \( x<-2 \) \( x<-30 \)

To solve the inequality \( -8x - 10 > 7x + 20 \), we start by moving all terms involving \(x\) to one side and constant terms to the other side. First, add \(8x\) to both sides: \[ -10 > 15x + 20 \] Next, subtract \(20\) from both sides: \[ -30 > 15x \] Now, divide both sides by \(15\) to isolate \(x\): \[ -2 > x \] This inequality can also be written as \(x < -2\). So, the correct solution to the inequality is: \(x < -2\). Now, to double-check: if we take a number less than \(-2\), like \(-3\), we can plug it back into the original inequality and confirm it holds true. Being able to rearrange and manipulate inequalities is vital; it opens up pathways to finding solutions without losing sight of the original question at hand. And remember, when multiplying or dividing by a negative number, flip that inequality sign!