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!!!
first. subtract 3/4 from each side.
i did that and i also wrote the answers next to each question and i just want to know if they are right.
are they right? please respond
#1 , #2 and #4 are correct. :)
for #3, you have two cases,
first: 7-x > 2 (positive case). thus,
-x > 2-7
-x > -5
x < 5
second: -(7-x) > 2 (negative case). thus,
-7+x > 2
x > 2+7
x > 9
thus, it should be x < 5and x > 9 or (-infinity, 5) U (9, +infinity)
*U = union*
sorry, I didn't understand.
are you sure?
thank you :)
it's okay i know it is kind of crowded :)
You're welcome! I'll explain how to get the answers to each of the given inequalities and equations:
1) To solve the inequality 3/4 + x > 1, you need to isolate the variable x. First, subtract 3/4 from both sides of the inequality: 3/4 + x - 3/4 > 1 - 3/4, which simplifies to x > 1/4.
2) For the inequality 10 - 3x < 5, again we need to isolate x. To do this, subtract 10 from both sides of the inequality: 10 - 3x - 10 < 5 - 10, which simplifies to -3x < -5. Now, divide both sides by -3. Remember that when you divide by a negative number, you need to reverse the inequality sign: -3x / -3 > -5 / -3. This gives us x > 5/3.
3) The inequality |7 - x| > 2 involves absolute values. To get rid of the absolute value sign, we will consider two cases: one where 7 - x is positive and another where it is negative.
Case 1: 7 - x > 2. Subtract 7 from both sides to isolate x: 7 - x - 7 > 2 - 7, which simplifies to -x > -5. Remember to flip the inequality sign when we divide by a negative number, giving us x < 5.
Case 2: -(7 - x) > 2. Multiply both sides by -1 to change the direction of the inequality: 7 - x < -2. Subtract 7 from both sides of the inequality: 7 - x - 7 < -2 - 7, which simplifies to -x < -9. Again, remember to flip the inequality sign when we divide by a negative number. This gives us x > 9.
Combining the solutions for both cases, we have x < 5 and x > 9. So the final answer is x > 9 OR x < 5.
4) Lastly, the equation |x + 0.5| = 0.25 involves absolute values. Remember that the absolute value of any number is always positive or zero. So, we can have two cases:
Case 1: x + 0.5 = 0.25. Subtract 0.5 from both sides: x + 0.5 - 0.5 = 0.25 - 0.5, which simplifies to x = -0.25.
Case 2: -(x + 0.5) = 0.25. Multiply both sides by -1 to change the direction of the inequality: x + 0.5 = -0.25. Subtract 0.5 from both sides: x + 0.5 - 0.5 = -0.25 - 0.5, which simplifies to x = -0.75.
So the final answers are x = -0.25 and x = -0.75.