First, group and combine like terms on the right side of the inequality:
#-37 < -5g + 3g - 7#
#-37 < (-5 + 3)g - 7#
#-37 < -2g - 7#
Next, add #color(red)(7)# to each side of the inequality to isolate the #g# term while keeping the inequality balanced:
#-37 + color(red)(7) < -2g - 7 + color(red)(7)#
#-30 < -2g - 0#
#-30 < -2g#
Now, divide each side of the inequality by #color(blue)(-2)# to solve for #g# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#(-30)/color(blue)(-2) color(red)(>) (-2g)/color(blue)(-2)#
#15 color(red)(>) (color(red)(cancel(color(black)(-2)))g)/cancel(color(blue)(-2))#
#15 > g#
To state the solution in terms of #g# we can reverse or "flip" the entire inequality:
#g < 15#
