Choose the correct solution and graph for the inequality. q+1/3>1/2 (1 point) q.1.6 Responses Image with alt text: q greater-than one sixth Image with alt text: A number line has an open circle at 1 over 6 and is filled in to the right. Image with alt text: q greater-than 1 Image with alt text: A number line has an open circle at 1 and is filled in to the right. Image with alt text: q greater-than five sixths Image with alt text: A number line has an open circle at 5 over 6 and is filled in to the right. Image with alt text: q less-than 0 Image with alt text: A number line has an open circle at 0 and is filled in to the left.
The correct solution and graph for the inequality q + 1/3 > 1/2 is:
q > 1/6
Image with alt text: q greater-than one sixth
Image with alt text: A number line has an open circle at 1 over 6 and is filled in to the right.
The correct solution and graph for the inequality q + 1/3 > 1/2 is q > 1/6.
The corresponding graph would be:
Image with alt text: A number line has an open circle at 1/6 and is filled in to the right.
To solve the inequality q + 1/3 > 1/2, you need to isolate q on one side of the inequality. Here are the steps to solve it:
1. Subtract 1/3 from both sides of the inequality:
q + 1/3 - 1/3 > 1/2 - 1/3
q > 1/2 - 1/3
2. Simplify the right side of the inequality:
q > 3/6 - 2/6
q > 1/6
So, the solution to the inequality is q > 1/6.
Now, let's graph this inequality on a number line:
- Draw a number line with a mark for 0 in the center.
- Put an open circle at 1/6 (since it is not included) and fill in the line to the right to represent all values greater than 1/6.
The correct graph for the inequality q + 1/3 > 1/2 would be:
Image: q greater-than one sixth
I hope this explanation helps!