Solve for x. show your work. -1/2 x < -12

2x − 3 < x + 2  
∴ x − 3 < 2  
∴ x < 5 

x + 2 ≤ 3x + 5 
∴ 2 ≤ 2x + 5 
∴ -3 ≤ 2x 
∴ -3/2 ≤ x 

-3/2 ≤ x < 5

First, is to divide both sides by the common denominator (2).

2 • -1/2x < -12•2

Now, you multiply the coefficients.
(Multiply 2 times -1)

2 • -1/2x < -12•2 = -2/2x < -12•2

Then, you divide -2 by 2 and that gives you -1

-1x < -12•2

Now, rewrite -1x as -x because “x” automatically identifies as “1” if there is no given number for “x” yet. Being that we are trying to solve for “x”.
(Also, because there is a “-“ sign present, that remains the same)

-x < -12•2

Now, we multiply -12 by 2.

-x < -24

Since we are solving for the positive variable, we will multiply each side by “-1”.

-x • -1 < -24 • -1
Which equals

x < 24

So your answer is x <24.

Hope this helps. :)

X>24