How do you solve #-3( x + 3) 7.5#?

Question

How do you solve #-3( x + 3) > 7.5#?

Eva Abramson · Accepted Answer

#x < -5.5#

First, expand the term within parenthesis on the left side of the inquality:

#-3x - (3*3) > 7.5#

#-3x - 9 > 7.5#

Next, add #color(red)(9)# to each side of the equation to isolate the #x# term while keeping the inequality balanced:

#-3x - 9 + color(red)(9) > 7.5 + color(red)(9)#

#-3x - 0 > 16.5#

#-3x > 16.5#

Now, we can divide each side by #color(blue)(-3)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality:

#(-3x)/color(blue)(-3) color(red)(<) 16.5/color(blue)(-3)#

#(color(blue)(cancel(color(black)(-3)))x)/cancel(color(blue)(-3)) color(red)(<) 16.5/color(blue)(-3)#

#x < 16.5/color(blue)(-3)#

#x < -5.5#

Eva Adamson · Answer

undefined To solve the inequality -3(x + 3) > 7.5: 1. Distribute -3 across the parentheses: -3x - 9 > 7.5 2. Add 9 to both sides: -3x > 16.5 3. Divide both sides by -3 (Note: Dividing by a negative number flips the inequality sign): x < -5.5 So, the solution to the inequality is x < -5.5.

How do you solve #-3( x + 3) &gt; 7.5#?

How do you solve #-3( x + 3) > 7.5#?