Solving One-Variable Inequalities — Quiz

Question 5 • Algebra I

Which number line represents the solution set for the inequality 2 x minus 6 is greater than or equal to 6 times open paren x minus 2 close paren plus 8 ?

Answer

Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at negative 0 point 5 and a bold line starts at negative 0 point 5 and is pointing to the right.

Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at positive 0 point 5 and a bold line starts at 0 point 5 and is pointing to the right.

Image with description A number line from negative 1 point 5 to positive 1 point 5 in increments of 0 point 5. A solid point is at positive 0 point 5 and a bold line starts at positive 0 point 5 and is pointing to the left.

Explanation

Expand the right side: 6(x − 2) + 8 = 6x − 4. Then 2x − 6 ≥ 6x − 4 simplifies to −2 ≥ 4x, so x ≤ −0.5. The solution is shown by a solid point at −0.5 with the line extending to the left, which is choice D.

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