What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
Answer: The solution set for x is x≥3.
Solving Linear Inequalities
To solve the inequality 2(3x – 1) ≥ 4x – 6, first expand and simplify it to get 6x – 2 ≥ 4x – 6. Then, solve for x, which results in x ≥ 3. Understanding and solving linear inequalities is crucial in algebra for representing and solving problems with a range of possible solutions. This concept is essential in various fields, including economics, engineering, and sciences, where conditions are represented by inequalities rather than exact values.
FAQ on Solving Linear Inequalities
How do you solve linear inequalities?
Isolate the variable on one side and interpret the inequality symbol.
What does the solution set of an inequality represent?
The solution set represents all possible values that satisfy the inequality.
How do you graph the solution set of an inequality?
Graph the corresponding equation, then shade the appropriate region based on the inequality.
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