Question

solve the inequality for x.
\\(\frac{x}{6} + 7 \geq 6\\)
simplify your answer as much as possible.

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( x \), we subtract 7 from both sides of the inequality \(\frac{x}{6}+7\geq6\). This gives us \(\frac{x}{6}+7 - 7\geq6 - 7\), which simplifies to \(\frac{x}{6}\geq - 1\).

Step2: Multiply both sides by 6

To solve for \( x \), we multiply both sides of the inequality \(\frac{x}{6}\geq - 1\) by 6. Since 6 is a positive number, the direction of the inequality sign remains the same. So we have \(\frac{x}{6}\times6\geq - 1\times6\), which simplifies to \(x\geq - 6\).

Answer:

\(x\geq - 6\)