Solve the inequality. Write the solution in set-builder notation.
-3(8x + 3) > - 9 - 24x
Starting with the given inequality:
-3(8x + 3) > -9 - 24x
Let's first distribute the -3 on the left side of the inequality:
-24x - 9 > -9 - 24x
Now let's simplify by subtracting -24x from both sides:
-24x - 24x - 9 > -9 - 24x - 24x
-48x - 9 > -9 - 48x
Next, let's simplify by adding 48x to both sides:
-48x + 48x - 9 > -9 - 48x + 48x
-9 > -9
This is a contradiction. The inequality -9 > -9 is not true for any value of x. Therefore, there is no solution to the inequality.
The solution in set-builder notation is an empty set:
{}
To solve the inequality -3(8x + 3) > - 9 - 24x, we will start by simplifying both sides of the inequality:
-3(8x + 3) > -9 - 24x
Distribute -3 to the terms inside the parentheses:
-24x - 9 > -9 - 24x
Next, we will simplify further by combining like terms:
-24x + 24x > -9 - 9
The -24x and +24x terms cancel each other out:
0 > -18
Since 0 is always greater than any negative number, this inequality holds true for all values of x. Thus, the solution to the inequality is the set of all real numbers, which can be written in set-builder notation as:
{x | x ∈ ℝ}
To solve the inequality -3(8x + 3) > -9 - 24x, we will first simplify the expression on both sides. Let's start by distributing -3 to the terms inside the parentheses:
-3 * 8x + -3 * 3 > -9 - 24x
-24x - 9 > -9 - 24x
Notice that we have -24x on both sides of the inequality. We can eliminate it by adding 24x to both sides:
-24x + 24x - 9 > -9 - 24x + 24x
-9 > -9
The inequality -9 > -9 is not true. In this case, there is no solution to the inequality. This means the solution set is empty (∅) or "no solution" in set-builder notation.