Problem 120 - Introductory and Intermediate Algebra for College Students 4th

Question

I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.

Step-by-Step Solution

Answer

-4 is indeed the greatest integer in the solution set of the inequality \(-2x + 5 \geq 13\).

Step 1: Solve the Inequality

Begin by solving the given inequality. Start by subtracting 5 from both sides, which gives \(-2x \geq 8\). Then divide both sides by -2. Remember that if you multiply or divide both sides of an inequality by a negative number, then you need to switch the direction of the inequality. Therefore we obtain \(x \leq -4\).

Step 2: Analyze the Solution Set

The solution to this inequality includes all real numbers that are less than or equal to -4. Therefore the greatest integer within this set would be -4.

Step 3: Check the Answer

By substituting -4 into the original inequality, we obtain \(-2*(-4) + 5 \geq 13\) which simplifies to \(8 + 5 \geq 13\) or \(13 \geq 13\), a true statement. Therefore, -4 is indeed the greatest integer that satisfies the inequality.