I am stuck on a few problems I multipled by the LCM to clear fractions but I keep getting confused can you help me with this problem?
3/4(3+2x)+2>17
and
8x-12<-9
3/4(3+2x)+2>17
multiply each term by 4
3(3+2x) + 8 > 68
9 + 6x > 60
6x > 51
x > 51/6
the second is really easy, add 12 to both sides, then divide by 8
That is what I did but I was told it was wrong...I got 3/8
8x-12<-9
8x < 12-9
8x < 3
x < 3/8
Was there a restriction on x, e.g. did it say x is an element of the integers or something like that?
No...this is why I am confused, they say the answer is 0
Sure, I'd be happy to help you with these problems!
Let's start with the first problem:
3/4(3+2x) + 2 > 17
To clear the fraction, we can multiply both sides of the inequality by the denominator of the fraction, which in this case is 4.
(3/4)(3+2x) + 2 > 17 --> 3(3+2x) + 8 > 68
Next, we can distribute the 3 to both terms inside the parentheses:
9 + 6x + 8 > 68
Combining like terms, we have:
6x + 17 > 68
To isolate the variable x, we can subtract 17 from both sides:
6x > 51
Finally, we can divide both sides by 6 to solve for x:
x > 8.5
Therefore, the solution to the inequality is x > 8.5.
Now let's move on to the second problem:
8x - 12 < -9
To isolate the variable x, we can start by adding 12 to both sides:
8x - 12 + 12 < -9 + 12
8x < 3
Lastly, we can divide both sides by 8 to find x:
x < 3/8 or x < 0.375
Therefore, the solution to the inequality is x < 0.375.
Remember, when solving inequalities, it's important to pay attention to the direction of the inequality sign when performing multiplication or division.