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Which of the following values are solutions to the inequality 
6x-3 >= 8 ?
I. 10
II. -5
III. -2
None
I only
II only
III only
I and II
I and III
II and III
I, II and III

Which of the following values are solutions to the inequality 6x38 6 x-3 \geq 8 ?\newlineI. 1010\newlineII. 5-5\newlineIII. 2-2\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III

Full solution

Q. Which of the following values are solutions to the inequality 6x38 6 x-3 \geq 8 ?\newlineI. 1010\newlineII. 5-5\newlineIII. 2-2\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III
  1. Isolate x by adding: Solve the inequality 6x386x - 3 \geq 8 for xx.\newlineFirst, add 33 to both sides of the inequality to isolate the term with xx on one side.\newline6x3+38+36x - 3 + 3 \geq 8 + 3\newlineThis simplifies to:\newline6x116x \geq 11
  2. Divide by 66: Now, divide both sides of the inequality by 66 to solve for xx.6x6116\frac{6x}{6} \geq \frac{11}{6}This simplifies to:x116x \geq \frac{11}{6}
  3. Check value I: Check if the value I (1010) is a solution to the inequality x116x \geq \frac{11}{6}.\newlineSubstitute x=10x = 10 into the inequality:\newline1011610 \geq \frac{11}{6}\newlineSince 1010 is greater than 116\frac{11}{6}, value I (1010) is a solution to the inequality.
  4. Check value II: Check if the value II (5-5) is a solution to the inequality x116x \geq \frac{11}{6}. Substitute x=5x = -5 into the inequality: 5116-5 \geq \frac{11}{6} Since 5-5 is not greater than 116\frac{11}{6}, value II (5-5) is not a solution to the inequality.
  5. Check value III: Check if the value III (2-2) is a solution to the inequality x116x \geq \frac{11}{6}. Substitute x=2x = -2 into the inequality: 2116-2 \geq \frac{11}{6} Since 2-2 is not greater than 116\frac{11}{6}, value III (2-2) is not a solution to the inequality.

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