Graph the inequality on the number line and then write it in interval notation.
Y+1/2≥2/3.
You would treat the greater than or equal to sign like an equation. So, you would subtract 1/2 from each side so y would be greater than or equal to 1/6. In interval notation it would be: [1/6, inf)
I hope it makes sense now ^-^
To graph the inequality Y + 1/2 ≥ 2/3 on a number line, follow the steps below:
Step 1: Start by plotting a point at the value -1/2 on the number line. This is because we have Y + 1/2 on the left side of the inequality.
Step 2: Since we have ≥, draw a solid line from the point you plotted in step 1 towards the right direction. This solid line indicates that Y + 1/2 can be equal to the given value.
Step 3: Finally, shade the region above the line because we have ≥. This means that any value of Y above the line will satisfy the inequality.
Next, let's write the inequality in interval notation.
Step 1: Subtract 1/2 from both sides of the inequality to isolate Y:
Y + 1/2 - 1/2 ≥ 2/3 - 1/2
Y ≥ 1/6
Step 2: Write the inequality using interval notation. In this case, since the inequality is only greater than or equal to, we use [ ] to indicate that the endpoint is included in the interval:
The final inequality in interval notation is: [1/6, ∞)
Therefore, the graph of the inequality and its interval notation representation is:
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