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Question

x/2 < 2/3 (x+3)

the x/2 and 2/3 are fractions. This problem is under Solving Inequalities with variables on both sides of the equation. I came up with the answer x >-0.444 and my dad tried it and he came up with x > -12

If you come up with an answer please show how you did it so i can see what happened. It's kinda complicated considering I have the hardest time with fractions in equations. I'd appreciate the help! Thanks guys!

Answer 1

x/2 < 2/3 (x + 3)
3x / 2 < 2 (x + 3)
3x < 4 (x + 3)
3x < 4x + 12
-x < 12
x > -12 (when you multiply by a negative number you MUST invert the inequality)

Answer 2

For starters, multiply both sides of the inequality by 2 to get rid of the fraction on the left. you'll get x < 4/3(x + 3)

Now multiply both sides by 3, which will get rid of the fraction on the right: 3x < 4(x + 3).

Now, use the distributive property: 3x < 4x + 12
Subtract 3x from both sides: 0 < x + 12
Subtract 12 from both sides: -12 < x, or x > -12.

So, see, your old-fogie daddy may know more than you give him credit for!!!

Answer 3

first u just have to pretend the inequality < or > is not there.. treat it as if it's an equal sign..but remember to flip the sign if u ever divide a side by a negative:

x/2 < 2/3(x+3)

get rid of the denominators, multiply both sides by 6:

3x < 4(x+3)

3x < 4x + 12

-x < 12

x > -12 (flipped!)

:)

Answer 4

multiply both sides by 2, expand the parentheses
x < (4/3)x + 4

Move the x terms to the same side
(-1/3)x < 4

Multiply by -3
x > -12

You can always verify that you have the right answer by substituting it back in for x in the original inequality and checking that its true.

Answer 5

(x/2) < (2/3)(x+3)

(x/2) < (2*(x+3) )/3

(x/2) < (2x/3 + 6/3)

(x/2) < (2x/3) + 2

x < (4x/3) + 4 ( Multiply by 2 both sides)

(x-4) < 4x/3

3x - 12 < 4x ( Multiply by 3 on both sides)

3x -4x -12 < 0 (Substract 4x on both sides)
-x -12 < 0

-x < 12

x > -12.....

Your dad was right.......