Solve the linear inequality. Express the solution using interval notation. $$ 5 x+21

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Solve the linear inequality. Express the solution using interval notation. $$ 5 x+21<6 $$ Graph the solution set.

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To solve the linear inequality $$ 5x + 21 < 6 $$, we'll follow these steps: ### Step 1: Solve the Inequality 1. **Subtract 21 from both sides** to isolate the term with $$ x $$: $$ 5x + 21 - 21 < 6 - 21 $$ $$ 5x < -15 $$ 2. **Divide both sides by 5** to solve for $$ x $$: $$ \frac{5x}{5} < \frac{-15}{5} $$ $$ x < -3 $$ ### Step 2: Express the Solution in Interval Notation The solution $$ x < -3 $$ can be written in interval notation as: $$ (-\infty,\, -3) $$ ### Step 3: Graph the Solution Set Here's how you can graph the solution on a number line: ``` <---|----------|----------|----------|---> -5 -4 -3 -2 ``` - **Open Circle at -3**: Since the inequality is strictly less than ($$ < $$) and does not include equality, we use an open circle at -3 to indicate that -3 is not part of the solution. - **Shade to the Left**: The solution includes all numbers less than -3, so we shade the number line to the left of -3. **Graphical Representation:** ``` <---|----------|----------|----------|---> -5 -4 (-3) -2 (Open circle at -3) <==== ``` - The arrow pointing to the left from -3 indicates all real numbers less than -3 are included in the solution set. ### Summary - **Solution:** $$ x < -3 $$ - **Interval Notation:** $$ (-\infty,\, -3) $$ - **Graph:** Number line with an open circle at -3 and shading extending to the left. The solution to the inequality $$ 5x + 21 < 6 $$ is $$ x < -3 $$, which in interval notation is $$ (-\infty,\, -3) $$.

Solve the linear inequality. Express the solution using interval notation. \[ 5 x+21<6 \] Graph the solution set.

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