I have two problems that Im.. having a problem with.
I would like an answer but with an step by step explanation, so i can do the other 20 that are due tomorrow... lol.
1. 3x - 8 > 10
2. -2x +7 ≤ 37
first question:
add 8 to each side, then divide both sides by 3
second:
add 2x to each side, subtract 37 from each side. Then, divide both sides by 2.
I remember doing this last year, so I'll try to tell you as much as I can remember.
My teacher told us last year to start of thinking of it like an equation. Pretend the greater or less than sign is a equals sign.
For #1, add 8 to both sides, like you would with an equation. For #2, take 7 away from both sides. If your inequality has the variable term (like 2x) on the right side instead of just a number, then you would take the variable terms away or add them first. Basically, move all the numbers to one side and variables to the other.
So now, for #1, you should have 3x > 18, and for #2, -2x < (sorry I can't underline the sign) 30.
Then, for #1, divide both sides by 3 like you would with an equation, to get it to be just x. That will make you get x > 6.
Here's a little tidbit from the algebra help book I am using: If you are dividing by an negative number, make sure you reverse the direction of the inequality, or basically reverse the sign. That's the part I always mess up on.
So, x > 6 would be your answer for #1. If you need any more help, or if you need help knowing how to graph the answer on a number line, you can post another response.
Hope I helped!
No problem, I can help you with both problems and provide step-by-step explanations. Let's start with problem 1.
1. 3x - 8 > 10
Step 1: Start by adding 8 to both sides of the inequality to isolate the variable term.
3x - 8 + 8 > 10 + 8
3x > 18
Step 2: Divide both sides of the inequality by 3 to solve for x.
(3x)/3 > 18/3
x > 6
So the solution to the inequality 3x - 8 > 10 is x > 6.
Now let's move on to problem 2.
2. -2x + 7 ≤ 37
Step 1: Begin by subtracting 7 from both sides of the inequality to isolate the variable term.
-2x + 7 - 7 ≤ 37 - 7
-2x ≤ 30
Step 2: Divide both sides of the inequality by -2. Remember that when dividing by a negative number, the direction of the inequality sign must be reversed.
(-2x)/-2 ≥ 30/-2
x ≥ -15
So the solution to the inequality -2x + 7 ≤ 37 is x ≥ -15.
Keep in mind that when solving inequalities, the rules are quite similar to equations, but when you multiply or divide both sides by a negative number, the inequality sign must be flipped. Additionally, when adding or subtracting a number from both sides of the inequality, the inequality sign remains unchanged.
I hope this explanation helps you tackle the remaining problems. Good luck!