Solve the inequality. Expression solution set using interval notation and graph the solution set using a number line. -15x+3<_-3(4x-7)
Thats supposed to be a greater than or equal to sign
-15x+3 ≤ -3(4x-7)
-15x + 3 ≤ -12x + 21
-3x ≤ 18
x ≥ -6
To solve the inequality -15x + 3 ≥ -3(4x - 7), we need to simplify and isolate the variable x. Let's solve it step by step:
First, distribute -3 to the terms inside the parentheses:
-15x + 3 ≥ -12x + 21
Next, combine like terms by adding 12x to both sides:
-3x + 3 ≥ 21
Then, subtract 3 from both sides:
-3x ≥ 18
Now, divide by -3, but remember that when dividing by a negative number, the inequality sign should be flipped:
x ≤ -6
The solution to the inequality is x ≤ -6.
To express this solution set using interval notation, we can write it as the interval (-∞, -6]. The square bracket [ indicates that the endpoint -6 is included in the solution set.
To graph the solution set on a number line, mark a closed circle at -6 and shade the line to the left, indicating all values less than or equal to -6. Here's a visual representation:
```
--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
●
```
In this case, the filled circle (●) represents -6, and the shaded portion to the left represents all values less than or equal to -6.