Answer:
Explanation:
To find the solution to the compound inequality 4x - 18 ≤ -x - 3 and -3x - 9 < -2 - 3, we need to solve each inequality separately and then find the intersection of their solutions.
Let's start with the first inequality: 4x - 18 ≤ -x - 3.
To isolate the variable x, we can add x to both sides:
4x + x - 18 ≤ -3.
Combining like terms gives us:
5x - 18 ≤ -3.
Next, we can add 18 to both sides to further isolate x:
5x - 18 + 18 ≤ -3 + 18.
Simplifying, we get:
5x ≤ 15.
Finally, we divide both sides by 5 to solve for x:
5x/5 ≤ 15/5.
The result is:
x ≤ 3.
Now let's move on to the second inequality: -3x - 9 < -2 - 3.
To isolate the variable x, we can add 3x to both sides:
-3x + 3x - 9 < -2 + 3x - 3.
Combining like terms gives us:
-9 < 3x - 5.
Next, we can add 5 to both sides to further isolate x:
-9 + 9 < 3x - 5 + 9.
Simplifying, we get:
0 < 3x + 4.
Finally, we can subtract 4 from both sides to solve for x:
0 - 4 < 3x + 4 - 4.
Simplifying, we get:
-4 < 3x.
Dividing both sides by 3, we get:
-4/3 < x.
Combining the solutions from both inequalities, we find that x must satisfy the condition:
x ≤ 3 and -4/3 < x.
Since the smaller value is -4/3, we can conclude that the solution to the compound inequality is:
x ≤ -4/3.
Therefore, the value that makes the statement true is x ≤ -4/3.