Which number line represents the solution the following inequally? $$ -8 x-3

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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

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1. Start with the inequality: $$ -8x - 3 < 18 - x $$ 2. Add $$8x$$ to both sides to eliminate the $$-8x$$ term on the left: $$ -8x - 3 + 8x < 18 - x + 8x \quad \Longrightarrow \quad -3 < 18 + 7x $$ 3. Subtract $$18$$ from both sides to isolate the term with $$x$$: $$ -3 - 18 < 18 - 18 + 7x \quad \Longrightarrow \quad -21 < 7x $$ 4. Divide both sides by $$7$$ (since $$7$$ is positive, the inequality direction remains the same): $$ \frac{-21}{7} < x \quad \Longrightarrow \quad -3 < x $$ 5. The inequality $$ -3 < x $$ can also be written as: $$ x > -3 $$ Thus, the solution to the inequality is $$ x > -3 $$. On a number line, this solution is represented by an open circle at $$-3$$ (indicating that $$-3$$ is not included) with a ray or shading extending to the right (representing all numbers greater than $$-3$$). The solution to the inequality $$-8x - 3 < 18 - x$$ is $$x > -3$$. On a number line, this is shown with an open circle at $$-3$$ and a ray extending to the right.

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

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