Solve the inequality. Graph the solution set and write it in interval notation.
6 left parenthesis 5 x plus 1 right parenthesis
less than6
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Part 1
Choose the correct graph below.
D.
An infinite number line labeled from negative 10 to 10, has tick marks in increments of 1. The region to the left of a right bracket at 6 is shaded.
-10-8-6-4-20246810
Part 2
Write the answer in interval notation.
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(Type your answer in interval notation.)
The correct graph is D. An infinite number line labeled from negative 10 to 10, has tick marks in increments of 1. The region to the left of a right bracket at 6 is shaded.
The solution set can be written in interval notation as (-∞, 6).
no
Apologies for the previous response.
Given the inequality 6(5x + 1) < 6, we can solve it as follows:
6(5x + 1) < 6
30x + 6 < 6
30x < 0
x < 0/30
x < 0
So the solution set is x < 0.
Graphically, we represent this on a number line by shading the region to the left of 0. The interval notation for this solution set is (-∞, 0).
To solve the inequality 6(5x + 1) < 6, we can follow these steps:
1. Distribute the 6 to both terms inside the parentheses:
30x + 6 < 6
2. Subtract 6 from both sides to isolate the variable:
30x < 0
3. Divide both sides by 30 to solve for x:
x < 0
Now let's graph the solution set and write it in interval notation:
The solution set for x < 0 can be represented on an infinite number line. Start by labeling the number line from negative infinity to positive infinity, and add tick marks in increments of 1.
Since x is less than 0, shade all the points to the left of 0, and leave 0 itself unshaded. Put a right bracket at 0 to indicate that it is not included in the solution set.
The correct graph is option D, which shows a right bracket at 0 and all points to the left shaded.
In interval notation, we write the solution set as (-∞, 0). This means that x can take any value less than 0, but 0 itself is not included.
So, the answer in interval notation is (-∞, 0).