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Chapter 2: Problem 120

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

Short Answer

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

Step by step solution

01

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 \(x \leq -4\).
02

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.
03

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.

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Most popular questions from this chapter

We know that \(|x|\) represents the distance from 0 to \(x\) on a number line. Use each sentence to describe all possible locations of \(x\) on a number line. Then rewrite the given sentence as an inequality involving \(|x|\). The distance from 0 to \(x\) on a number line is greater than 2 .

Simplify: \(-16-8 \div 4 \cdot(-2) .\) (Section \(1.8,\) Example 4 )

Solve each inequality. Use a calculator to help with the arithmetic. $$126.8-9.4 y \leq 4.8 y+34.5$$

It is possible to have a circle whose circumference is numerically equal to its area.

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$4(2 y-1)>12$$
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