1)3/4+x>1 answer:x>1/4
2)10-3x<5 answer:x>5/3
3)|7-x|>2 answer:x>-5 x<-9
4)|x+0.5|=0.25 answer:x=-o.25,-0.75
thank you very very much!!!
Prob.1 and 2 are correct.
3. [7 - x] > 2.
Eq1: +(7 - x) > 2. Eq2: -(7 - 7)>2.
Eq1: +(7 - x) > 2,
7 - x > 2,
-x > 2 - 7,
-x > -5,
Divide both sides by -1 and reverse inequality sign:
x < 5.
Eq2: -(7 - x) > 2.
-7 + x > 2,
x > 2 + 7,
x > 9.
Solution set: x < 5, and x > 9.
Therefore, all values of x < 5 and
> 9 shuld satisfy the inequality.
Values of x between 5 and 9 should not
satisfy the inequality.
Eq3: 5 > x > 9.
4. CORRECT!!
You did great! you missed only one.
You forgot to reverse the inequality sign when you divided by -1.
Most students would have missed 3 and 4.
You're welcome! I'm glad I could help. Now, let me explain how I arrived at the solutions for each of the given inequalities.
1) To solve the inequality 3/4 + x > 1, we need to isolate the variable x.
First, we subtract 3/4 from both sides to get:
3/4 + x - 3/4 > 1 - 3/4
This simplifies to:
x > 1/4
So, the solution to the inequality is x > 1/4.
2) To solve the inequality 10 - 3x < 5, we again need to isolate the variable x.
First, we subtract 10 from both sides to get:
10 - 3x - 10 < 5 - 10
This simplifies to:
-3x < -5
Next, we divide both sides by -3, remembering that when we divide by a negative number, the inequality sign flips:
x > 5/3
So, the solution to the inequality is x > 5/3.
3) To solve the inequality |7 - x| > 2, we consider two cases:
Case 1: 7 - x > 2
In this case, we subtract 7 from both sides to get:
7 - x - 7 > 2 - 7
This simplifies to:
-x > -5
Next, when we multiply or divide by a negative number, the inequality sign flips:
x < -5
Case 2: -(7 - x) > 2
In this case, we distribute the negative sign to both numbers inside the absolute value:
-x + 7 > 2
Next, we subtract 7 from both sides to get:
-x + 7 - 7 > 2 - 7
This simplifies to:
-x > -5
Again, when we multiply or divide by a negative number, the inequality sign flips:
x < -5
So, the solutions to the inequality are x > -5 and x < -9.
4) To solve the equation |x + 0.5| = 0.25, we consider two cases:
Case 1: x + 0.5 = 0.25
In this case, we subtract 0.5 from both sides to get:
x + 0.5 - 0.5 = 0.25 - 0.5
This simplifies to:
x = -0.25
Case 2: -(x + 0.5) = 0.25
In this case, we distribute the negative sign to both numbers inside the absolute value:
-x - 0.5 = 0.25
Next, we add 0.5 to both sides to get:
-x - 0.5 + 0.5 = 0.25 + 0.5
This simplifies to:
-x = 0.75
Finally, when we multiply or divide by a negative number, the inequality sign flips:
x = -0.75
So, the solutions to the equation are x = -0.25 and x = -0.75.
I hope this explanation helps! If you have any more questions, feel free to ask.