How do you solve and write the following in interval notation: #-2/5

Question

How do you solve and write the following in interval notation: #-2/5< -4/5x#?

Avery Alexander · Accepted Answer

See a solution process below:

Multiply each side of the inequality by #color(blue)((5/-4)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator: #color(blue)(5/-4) xx (-2)/5 color(red)(>) color(blue)(5/-4) xx (-4)/5x# #(-10)/-20 color(red)(>) color(blue)(color(black)(cancel(color(blue)(5)))/color(black)(cancel(color(blue)(-4)))) xx color(blue)(cancel(color(black)(-4)))/color(blue)(cancel(color(black)(5)))x# #1/2 > x# Or, to state the inequality in terms of #x# we can reverse or "flip" the entire inequality: #x < 1/2# And, in interval notation: #(-oo, 1/2)#

Nathan Axel · Answer

undefined To solve and write the inequality -2/5 < -4/5x in interval notation, you first isolate x. Divide both sides by -4/5, but remember to reverse the inequality sign since you're dividing by a negative number. -2/5 < -4/5x -2/5 / (-4/5) > x (5/4)(-2/5) > x -1/2 > x So, the solution is x < -1/2. In interval notation, this is represented as (-∞, -1/2).

How do you solve and write the following in interval notation: #-2/5&lt; -4/5x#?

How do you solve and write the following in interval notation: #-2/5< -4/5x#?