#5(2x+3) > 4(x-2) - 13#
Solving inequalities is similar to solving equations.
First, use the distributive property (shown below) to simplify #color(blue)(5(2x+3))# and #color(blue)(4(x-2))#:
Following this image, we know:
#color(blue)(5(2x+3) = (5 * 2x) + (5 * 3) = 10x + 15)#
#color(blue)(4(x-2) = (4 * x) + (4 * -2) = 4x - 8)#
Let's put these back into the inequality:
#10x + 15 > 4x - 8 - 13#
Combine #color(blue)(-8-13 => -21)#:
#10x + 15 > 4x - 21#
Subtract #color(blue)15# from both sides of the inequality:
#10x + 15 quadcolor(blue)(-quad15) > 4x - 21 quadcolor(blue)(-quad15)#
#10x > 4x -36#
Subtract #color(blue)(4x)# from both sides of the inequality:
#10x quadcolor(blue)(-quad4x) > 4x - 36 quadcolor(blue)(-quad4x)#
#6x > -36#
Divide both sides by #color(blue)(6)#:
#(6x)/color(blue)6 > -36/color(blue)6#
#x > -6#
This means #x# is greater than #-6#.
Hope this helps!
