How do you solve #Solve: 1/2x - 3

Question

How do you solve #Solve: 1/2x - 3 <=-1/1.5x - .5 <=1/2x + 2#?

Savannah Anderson · Accepted Answer

Given #1/2x-3 <= -1/1.5x =.5 <= 1/2x+2# Simplify by multiplying each expression by #6# to clear the fractions (Remember that you can multiply by any value greater than zero without effecting the orientation of the inequalities).
#3x-9 <= -4x-3 <= 3x+12# Break this up into two compound inequalities:
#"[1]        "3x-9<=-4x-3#
and
#"[2]        "-4x-3<=3x+12# Evaluate Inequality [1]
#3x-9<=-4x-3#
#color(white)("MMMMMM")#Add #(4x+9)# to both sides:
#7x <= 6#
#color(white)("MMMMMM")#Divide by #7# (which does not change the inequality orientation)
#x<=6/7# Evaluate Inequality [2]
#-4x-3 <= 3x+12#
#color(white)("MMMMMM")#Add #(4x-12)# to both sides
#-15<= 7x#
#color(white)("MMMMMM")#Divide both sides by 7
#(-15/7)<=x# Combine the Compound Inequalities (with and)
#x<=6/7# and #x>= (-15/7)#
#color(white)("MMMMMM")#Re-write as a single compound statement
#(-15/7) <= x <= 6/7#

Jameson Allen · Answer

undefined To solve the inequality $ \frac{1}{2}x - 3 \leq -\frac{1}{1.5}x - 0.5 \leq \frac{1}{2}x + 2 $, follow these steps:

1. Subtract $ \frac{1}{2}x $ from all parts of the inequality.
2. Add $ 0.5 $ to all parts of the inequality.
3. Solve each individual inequality.
4. Check if the solutions satisfy all three inequalities simultaneously.

The solution is $ x \leq -8 $ and $ x \geq 4 $.

How do you solve #Solve: 1/2x - 3 &lt;=-1/1.5x - .5 &lt;=1/2x + 2#?

How do you solve #Solve: 1/2x - 3 <=-1/1.5x - .5 <=1/2x + 2#?