Question

solve the inequality \\(\frac{x}{-2} + 7 > 12\\).
\\(x\\) ? ?

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( x \), we subtract 7 from both sides of the inequality \(\frac{x}{-2}+7 > 12\). This gives us \(\frac{x}{-2}+7 - 7>12 - 7\), which simplifies to \(\frac{x}{-2}>5\).

Step2: Multiply both sides by -2 (and reverse inequality)

When we multiply or divide both sides of an inequality by a negative number, we must reverse the direction of the inequality sign. So, multiplying both sides of \(\frac{x}{-2}>5\) by -2, we get \(x < 5\times(-2)\) (note the inequality sign is reversed from \(>\) to \(<\)). Calculating the right - hand side, \(5\times(-2)=- 10\). So \(x < - 10\).

Answer:

\(x < - 10\)