Solve the inequality. Graph the solution set and write it in interval notation.
5(4x + 1) < 5
Write the answer in interval notation.
__ (Type your answer in interval notation.)
The first step is to simplify the inequality. We'll start by distributing the 5 on the left side:
5(4x + 1) < 5
20x + 5 < 5
Now, let's isolate the variable on one side of the inequality. We'll subtract 5 from both sides:
20x + 5 - 5 < 5 - 5
20x < 0
Finally, we'll divide both sides by 20 to solve for x:
20x/20 < 0/20
x < 0
The solution set is all values of x that are less than 0.
In interval notation, this can be written as: (-∞, 0).
To solve the inequality 5(4x + 1) < 5, we will follow these steps:
Step 1: Distribute the 5 on the left side of the inequality:
20x + 5 < 5
Step 2: Subtract 5 from both sides of the inequality:
20x < 0
Step 3: Divide both sides of the inequality by 20:
x < 0
The solution to the inequality is x < 0. We can graph this solution on a number line as an open circle at 0, and shade the region to the left of 0.
In interval notation, the solution set is (-∞, 0). The parentheses indicate that the interval does not include 0, and the negative infinity symbol shows that the solution set extends indefinitely to the left.
To solve the inequality 5(4x + 1) < 5, you can follow these steps:
Step 1: Distribute the 5 to the terms inside the parentheses:
20x + 5 < 5
Step 2: Simplify the inequality:
20x < 0
Step 3: Divide both sides of the inequality by 20 to isolate x:
x < 0/20
x < 0
Now that we have solved the inequality, we can graph the solution set:
On a number line, mark the point 0 and shade all the values to the left of 0. This indicates that x is less than 0.
```
-∞ 0
──|─────○────
```
To write the solution set in interval notation, we can write it as (-∞, 0). The parenthesis indicates that the endpoint values are not included in the interval and the "-" symbol represents all possible values less than 0.