How do you solve and write the following in interval notation: #1 + 5x ≤ 11#?
Solution:
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The solution is
The formula is
Let's construct a sign chart.
Consequently,
and
The resolution is
graph{1+5x11 [15.95, 397, 12.05, 15.09]}
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Solution to
Interval Notation:
Given the inequality:
There are two possible cases:
Case 1:
Case 2:
Case 1:
Subtract
Divide both sides of the inequality by
Case 2:
Subtract
Divide both sides of the inequality by
Combine both the solutions: Solution 1 and Solution 2
You can also rewrite the combined solution as:
In Interval Notation:
Graph the inequality to verify our solution:
Hope it helps.
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To solve the inequality ( 1 + 5x \leq 11 ) and write it in interval notation:

Solve for the two cases: a) ( 1 + 5x \leq 11 ) b) ( (1 + 5x) \leq 11 )

Solve each case for ( x ): a) ( 5x \leq 10 ) b) ( 5x \leq 12 )

Divide each side by 5 for both cases: a) ( x \leq 2 ) b) ( x \geq \frac{12}{5} )

Combine the solutions: The solution in interval notation is ( \left[\frac{12}{5}, 2\right] ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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