An infinite number line labeled from negative 2 to 10, has tick marks in increments of 1. A shaded region exists to the right of a left parenthesis at 0 and the left of a right bracket between 3 and 4 labeled StartFraction 11 Over 3 EndFraction.
-2-1012345678910
11 divided by 3
Write the solution in interval notation.
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
The shaded region is to the right of 0 and to the left of StartFraction 11 Over 3 EndFraction.
In interval notation, this is written as:
(0, StartFraction 11 Over 3 EndFraction]
Explanation:
- The left parenthesis at 0 indicates that 0 is not included in the interval.
- The right bracket between 3 and 4 labeled StartFraction 11 Over 3 EndFraction indicates that StartFraction 11 Over 3 EndFraction is included in the interval.
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I apologize for any confusion. Let's correct the solution.
The shaded region is to the right of 0 and to the left of StartFraction 11 Over 3 EndFraction.
In interval notation, this is written as:
(0, StartFraction 11 Over 3 EndFraction)
Explanation:
- The left parenthesis at 0 indicates that 0 is not included in the interval.
- The right parenthesis at StartFraction 11 Over 3 EndFraction indicates that StartFraction 11 Over 3 EndFraction is not included in the interval.
To find the shaded region between the left parenthesis at 0 and the left bracket between 3 and 4, we need to determine the range of values that fall within this shaded region.
Starting with the left parenthesis at 0, we need to consider all values greater than 0. This means our shaded region starts at 0 and continues indefinitely to the right.
Next, we need to consider the right bracket between 3 and 4 labeled as StartFraction 11 Over 3 EndFraction. To convert this fraction to a decimal, we divide 11 by 3:
11 ÷ 3 ≈ 3.6667
Since our number line is labeled only up to 10, but the shaded region extends indefinitely to the right, we can conclude that the shaded region continues up to infinity but stops just before the number 4.
Therefore, the shaded region can be represented in interval notation as:
[0, 4)
The left bracket indicates that the value 0 is included in the shaded region, while the right parenthesis indicates that the value 4 is not included.