Question

which of the following is equivalent to $1 - 2x > 3(x - 2)$?
a. $1 - 2x > 3x - 2$
b. $1 - 2x > 3x - 5$
c. $1 - 2x > 3x - 6$
d. $1 - 2x > 3x - 7$

Explanation:

Step1: Expand the right side

To simplify \(3(x - 2)\), we use the distributive property \(a(b - c)=ab - ac\). Here, \(a = 3\), \(b=x\), and \(c = 2\). So, \(3(x - 2)=3\times x-3\times2=3x - 6\).

Step2: Substitute back

Substituting the expanded form back into the original inequality \(1-2x>3(x - 2)\), we get \(1 - 2x>3x - 6\).

Answer:

C. \(1 - 2x>3x - 6\)