Can some one help me solve this???

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3/4(3x-1/2)<4
3x-12<16/3
3x<52/3
x<52/9

You can treat the inequality like an = sign
You just simplify the inequality:
3/4(3X-12) < 12/3
9/4X - 8 < 4
9/4X <12
9X < 3
X < 3

(3/4)(3x - 1/2) - 7/3 < 5/3
3(3x - 1/2)/4 < 5/3 + 7/3
(9x - 3/2)/4 < 12/3
9x - 3/2 < 4(4)
9x - 3/2 < 16
2(9x - 3/2) < 2(16)
18x - 3 < 32
18x < 32 + 3
18x < 35
x < 35/18

3/4 (3x-1/2) -7/3<5/3
First, add 7/3 to both sides of your inequality (this will simplify a lot ...)
3/4 (3x-1/2) -7/3<5/3
+7/3 +7/3
3/4(3x-1/2) < 12/3 ... (12/3 = 4 )
3/4 (3x-1/2) < 4
Next multiply both sides of your inequality by 4
4 * 3/4 (3x-1/2) < 4*16
3(3x -1/2) < 16
Distribute the 3
9x - 3/2 < 16
Multiply everything by 2
2 * 9x - 3/2 < 16 *2
18x - 3 < 32
add 3
18x < 35
Divide by 18
x = 1.94

CHECK: 3/4[ 3(1.94)-1/2) -7/3 < 5/3
add the 7/3 again
3/4(3x-1/2) < 12/3
convert the 3/4 & 1/2 to decimals (3/4 =.75, 1/2 =.5)
.75[(3)(1.94) - .5] < 4
.75 (5.82)-(.5) < 4
.75 (5.32) < 4
3.99 < 4
(there was some rounding, ie 35/18 = 1.944444444 ... however, the answer checks out)
x < 1.94 <---- ANSWER

That was a hard one, all those different denominators ... just begging you to make a mistake !! Good Luck, hope I helped.

****just checked back in, only "the nerd" got it right, everyone else mistook the 1/2 for a 12 at one point or another ... that's why you always do a check ... and for the purposes of doing a check, consider the < or > an = sign, it's the only way to be sure. A lot of numbers fulfill the < then or > then criteria.

Hi.

The 3/4 is multiplied by the stuff in parenthesis, right? If so,

9x/4 - 3/8 - 7/3 < 5/3

9x/4 < 5/3 + 7/3 + 3/8

x < 35/18 [[Check my work; doing fractions in my head![[