Which number line represents the solution the following inequally? \[ -8 x-3<18-x \] A) B) C) \[ \begin{array}{l} \text { D) } \end{array} \] © Amazing Mathematics

To solve the inequality \(-8x - 3 < 18 - x\), we first isolate \(x\). Adding \(x\) to both sides gives us \(-8x + x < 18 + 3\), which simplifies to \(-7x < 21\). Dividing both sides by \(-7\) (remember, reversing the inequality sign) leads us to \(x > -3\). This means any number greater than \(-3\) is part of the solution, and on a number line, it would be represented with an open circle at \(-3\) and shading to the right. The key takeaway here is understanding how to reverse the inequality when dividing or multiplying by a negative number—this can trip up many budding mathematicians! Remember, always keep an eye on the sign when making those calculations. To dive deeper into inequalities, consider exploring resources that not only break down the concept with visual aids but also include practice problems to solidify your understanding. Websites like Khan Academy or educational YouTube channels often provide excellent insights and engaging explanations!