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 lol

See previous post.

To solve the inequality -15x + 3 ≥ -3(4x - 7), we will follow these steps:

Step 1: Distribute -3 on the right side of the equation: -15x + 3 ≥ -12x + 21

Step 2: Combine like terms: -15x + 3 ≥ -12x + 21 can be rewritten as -15x + 12x ≥ 21 - 3, which simplifies to -3x ≥ 18.

Step 3: Divide both sides of the inequality by -3, remembering to flip the inequality sign when dividing by a negative number: x ≤ 18 / -3

Step 4: Simplify the result: x ≤ -6

Now we can express the solution set using interval notation and graph it on a number line.

The solution set in interval notation is (-∞, -6]. On the number line, we mark a closed circle at -6 and shade to the left side.

Here is a graph to represent the solution set:

```
---o===========================
-6
```

The shaded portion to the left of -6 indicates all the values of x that satisfy the inequality.

To solve the inequality -15x+3 ≥ -3(4x-7), we will start by simplifying both sides of the equation and then isolating the variable x.

Step 1: Simplify the inequality
-15x+3 ≥ -12x+21

Step 2: Move all variables to one side of the inequality
-15x+12x ≥ 21-3
-3x ≥ 18

Step 3: Divide by the coefficient of x (which is -3) to isolate the variable x. Note that when dividing an inequality by a negative value, the inequality sign will be flipped.
x ≤ 18/-3
x ≤ -6

Now, let's express the solution set in interval notation and graph it on a number line:

Interval Notation: (-∞, -6]

To graph the solution set on a number line:
1. Mark a point on the number line at -6.
2. Draw a closed circle at -6 to indicate inclusivity.
3. Shade the line to the left of -6, indicating all the values from negative infinity up to and including -6.

Here's a visual representation:

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