Question

Difficulty: EasyLinear Inequalities in One Variable

If 2(x5)4-2(x - 5) \geq 4, what is the maximum possible value of xx?

Answer: 3

Answer

3
Distributing the 2-2 on the left side of the inequality 2(x5)4-2(x - 5) \geq 4 yields 2x+104-2x + 10 \geq 4. Subtracting 1010 from both sides gives 2x6-2x \geq -6. Dividing both sides by 2-2 and reversing the inequality sign results in x3x \leq 3. The maximum possible value is therefore 3.

Step-by-Step Solution

1
Distribute 2-2 to the terms inside the parentheses.
2x+104-2x + 10 \geq 4
Applying the distributive property simplifies the inequality.
2
Subtract 1010 from both sides of the inequality.
2x6-2x \geq -6
This isolates the variable term on the left side.
3
Divide both sides of the inequality by 2-2 and reverse the inequality sign.
x3x \leq 3
Dividing both sides of an inequality by a negative number reverses the direction of the inequality.

Key Concept

Solving linear inequalities in one variable using the distributive property and division by negative numbers.
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