First, expand the terms in parenthesis on the left side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:
color(red)(2)(3x - 1) >= 4x - 62(3x−1)≥4x−6
(color(red)(2) * 3x) - (color(red)(2) * 1) >= 4x - 6(2⋅3x)−(2⋅1)≥4x−6
6x - 2 >= 4x - 66x−2≥4x−6
Next, add color(red)(2)2 and subtract color(blue)(4x)4x from each side of the inequality to isolate the xx term while keeping the inequality balanced:
-color(blue)(4x) + 6x - 2 + color(red)(2) >= -color(blue)(4x) + 4x - 6 + color(red)(2)−4x+6x−2+2≥−4x+4x−6+2
(-color(blue)(4) + 6)x - 0 >= 0 - 4(−4+6)x−0≥0−4
2x >= -42x≥−4
Now, divide each side of the inequality by color(red)(2)2 to solve for xx while keeping the inequality balanced:
(2x)/color(red)(2) >= -4/color(red)(2)2x2≥−42
(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) >= -2
x >= -2
