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Question

Difficulty: MediumLinear Inequalities in One Variable

If −3(2x−5)+4x≥−7-3(2x - 5) + 4x \geq -7, what is the maximum possible value of xx?

Answer: 11

Answer

The maximum possible value of xx is 1111.
By applying the distributive property, combining like terms, and dividing by −2-2 (while reversing the inequality sign), we find that the solution is x≤11x \leq 11. Thus, the maximum possible value of xx is 1111.

Step-by-Step Solution

1
Apply the distributive property to simplify the left side of the inequality.
−6x+15+4x≥−7 -6x + 15 + 4x \geq -7
Multiplying −3-3 by each term inside the parentheses (2x−5)(2x - 5) yields −6x-6x and +15+15.
2
Combine the variable terms on the left side.
−2x+15≥−7 -2x + 15 \geq -7
Combining −6x-6x and 4x4x gives −2x-2x.
3
Subtract 1515 from both sides of the inequality.
−2x≥−22 -2x \geq -22
To isolate the variable term −2x-2x on the left side.
4
Divide both sides by −2-2 and flip the inequality sign.
x≤11 x \leq 11
Dividing both sides of an inequality by a negative number reverses the direction of the inequality sign.
5
Determine the maximum value from the solution set.
11
The solution set consists of all values less than or equal to 1111, so the greatest value is 1111.

Key Concept

Solving multi-step linear inequalities, including applying the distributive property and reversing the inequality sign when dividing by a negative number.
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Topics

Linear Inequalities in One Variable

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