Question

Solve the inequality. $$15-x<7$$

Short answer

The solution to the inequality is \(x > 8\).

Step-by-step solution

Analyze the Inequality

The inequality given is \(15 - x < 7\). The goal is to isolate \(x\) on one side of the inequality.

Subtract 15 from Both Sides

Subtract 15 from both sides to isolate \(-x\). This gives the inequality \(-x < 7 - 15\). Remember, when we subtract 15 from both sides, the inequality sign remains the same.

Simplify the Right Side

Simplify the right side of the inequality. This gives the inequality \(-x < -8\).

Divide Both Sides by -1

Finally, divide both sides of the inequality by -1 to solve for \(x\). Remember that when dividing or multiplying by a negative number in an inequality, the direction of the inequality sign changes. This gives the final inequality \(x > 8\).