Solve and Graph:
( i know that second part would be difficult but can you possibly explain it more)
-3©¦x+4©¦-5 ¡Ý 10
Please explain. I would really appreciate it. I'm not in school, i'm homebound and mom will not allow me to attend tutuoring at school for help even though they say I can. I would very much appreciate the help. Any and all you can give.
Please and thank you!
I'm sorry to hear that you're having difficulty accessing tutoring, but I'm here to help you with this math problem. Don't worry, I'll guide you through the solution step by step.
To solve the inequality -3|x + 4| - 5 ≥ 10, we can follow these steps:
Step 1: Simplify the given inequality.
The first step is to simplify the absolute value expression. Remember that the absolute value of a number is its distance from zero on the number line. So, when x + 4 is positive, -3|x + 4| turns into -3(x + 4), and when x + 4 is negative, -3|x + 4| becomes -3(-(x + 4)), which simplifies to 3(x + 4).
Now let's rewrite the inequality:
-3(x + 4) - 5 ≥ 10
Step 2: Solve the equation.
To solve the equation, we need to isolate the variable x. Let's begin by simplifying the left side of the inequality:
-3x - 12 - 5 ≥ 10
Combine like terms:
-3x - 17 ≥ 10
Step 3: Isolate the variable.
To isolate x, we need to get rid of the constant term -17 on the left side of the inequality. We can do this by adding 17 to both sides:
-3x - 17 + 17 ≥ 10 + 17
The -17 and +17 on the left side cancel out:
-3x ≥ 27
Step 4: Solve for x.
Now we can solve for x by dividing both sides of the inequality by -3. Remember, whenever we divide or multiply an inequality by a negative number, we need to reverse the inequality sign:
-3x/(-3) ≤ 27/(-3)
This simplifies to:
x ≤ -9
Therefore, the solution to the inequality is x ≤ -9.
Now, let's move on to graphing the inequality:
To graph the inequality x ≤ -9, we can represent it on a number line.
1. Draw a number line and label it accordingly, placing -9 on it.
2. Since the inequality includes values less than or equal to -9, we fill in a closed circle or solid dot at -9.
3. Shade the number line to the left of -9 to represent all the values of x that are less than or equal to -9.
This graph visually represents the values of x that satisfy the inequality x ≤ -9.