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
Oh, inequality problems! Time to get this party started! Let's solve this one-step at a time, putting a smile on your face along the way. So, let the fun begin!
First, let's distribute the -3 on the right side of the inequality:
-15x + 3 ≤ -12x + 21
Next, let's collect like terms by adding 12x to both sides:
-15x + 12x + 3 ≤ -12x + 12x + 21
Simplify that and what do you have?
-3x + 3 ≤ 21
Now, let's subtract 3 from both sides:
-3x + 3 - 3 ≤ 21 - 3
That's -3x ≤ 18.
To make our lives easier, let's divide both sides by -3 (oh, the sweet taste of division):
-3x/(-3) ≥ 18/(-3)
Guess what, my friend? When you divide or multiply an inequality by a negative number, the direction changes. So we get:
x ≥ -6
Now that we've found the solution, let's put it in interval notation: [-6, ∞).
And just for kicks, let's graph it on a number line. Picture a number line with a smiley face emoji on the right side, representing positive infinity. And starting from -6, draw a ray going to the right, because x is greater than or equal to -6.
Voila! Problem solved, fun had, and smiles shared. Keep on rocking those inequalities! 🎉
To solve the inequality -15x + 3 ≥ -3(4x - 7), we need to simplify and isolate x.
Step 1: Distribute the -3 on the right side of the inequality:
-15x + 3 ≥ -12x + 21
Step 2: Combine like terms on both sides:
-15x + 3 + 12x ≥ -12x + 21 + 12x
Step 3: Simplify:
-3x + 3 ≥ 21
Step 4: Subtract 3 from both sides:
-3x + 3 - 3 ≥ 21 - 3
Step 5: Simplify:
-3x ≥ 18
Step 6: Divide both sides by -3. Note that dividing by a negative number flips the inequality sign:
-3x/(-3) ≤ 18/(-3)
Simplifying, we get:
x ≤ -6
The solution to the inequality is x ≤ -6.
Using interval notation, the solution set is (-∞, -6], which means any value of x that is less than or equal to -6.
Graphically, we would represent the solution set on a number line by shading all the points to the left of and including -6.
To solve the inequality -15x + 3 ≥ -3(4x - 7), we need to simplify and isolate the variable x. Let's go step by step:
1. Distribute -3 through (4x - 7) on the right side of the inequality:
-15x + 3 ≥ -12x + 21
2. Combine like terms on both sides of the inequality:
-15x + 3 + 12x ≥ 21
Simplifying, we get:
-3x + 3 ≥ 21
3. Subtract 3 from both sides of the inequality:
-3x + 3 - 3 ≥ 21 - 3
Simplifying, we get:
-3x ≥ 18
4. Divide both sides of the inequality by -3. Since we are dividing by a negative number, the inequality sign will flip:
-3x/(-3) ≤ 18/(-3)
Simplifying, we get:
x ≤ -6
Now we have the solution for x. To express the solution set using interval notation and graph it on a number line:
Interval notation: (-∞, -6]
Number Line:
--------------------------●
-15x+3 >= -3(4x-7).
-15x+3 >= -12x+21.
-15x + 12x >= 21-3.
-3x >= 18.
X <= -6.
When multiplying or dividing an
inequality by a negative number,
the inequality sign should be reversed.