Question

Yuma is solving the inequality 3x−23≥−5
.

To solve the inequality, he begins by solving the equation as shown.

Which number line represents the solution to the inequality?

3 x minus 23 = negative 5. Add 23 to both sides and divide by 3. StartFraction 3 x Over 3 EndFraction = StartFraction 18 Over 3 EndFraction. x = 6.
CLEAR CHECK

(A)A number line going from 0 to 20. A closed circle is at 6.

(B) A number line going from 0 to 20. A closed circle is at 6. The line is shaded from the circle to the left.

(C) A number line going from 0 to 20. Closed circles are at 2 and 10. The line is shaded between the 2 circles.

(D)A number line going from 0 to 20 in increments of 1. Points are at 2 and 10. A line goes from point 2 to point 10.

Answer 1

The correct answer is (B) A number line going from 0 to 20. A closed circle is at 6. The line is shaded from the circle to the left.

Since the inequality is 3x - 23 ≥ -5, we solve for x by adding 23 to both sides, which gives us 3x ≥ 18. Then, we divide both sides by 3 to find x, which gives us x ≥ 6. This means that any value of x equal to or greater than 6 satisfies the inequality. Therefore, the number line should be shaded from the closed circle at 6 to the left to show all the values greater than or equal to 6.