# Inequality intersection help

## Homework Statement

$$|2x-1|+|x+2|\geq 4x$$

## The Attempt at a Solution

For x<-2 , $$-(2x-1)-(x+2)\geq 4x$$

$$x\leq -\frac{1}{7}$$

For $$x\geq \frac{1}{2}$$

$$2x-1+x+2\geq 4x$$

$$x\leq 1$$

For $$-2 \leq x < \frac{1}{2}$$ ,

$$-(2x-1)+x+2\geq 4x$$

$$x\leq \frac{3}{5}$$

after combining , the solution would be $$x\leq -\frac{1}{7}$$

AM i correct ? but the answer given is $$x\leq 1$$

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
Hi thereddevils!

Your three answers are correct, but you're not putting them together correctly.

For example, you have:

if x ≤ -2, it's true for x ≤ -1/7.

so it's true for all x ≤ -2.

ok, now try the others.

Hi thereddevils!

Your three answers are correct, but you're not putting them together correctly.

For example, you have:

if x ≤ -2, it's true for x ≤ -1/7.

so it's true for all x ≤ -2.

ok, now try the others.

thanks tiny , yeah , i am confused with the last part , what i did is to put x<= -1/7 , x<=1 , x<= 3/5 on the number line and take the intersection which is what i got .

so say for x>= 1/2 , x can be 4 , x<=1 , so 4<=1 ?? this is not true

i am sorry , i still do not understand the last part .

tiny-tim
Science Advisor
Homework Helper
There are three possibilities:

x ≤ -2, -2 ≤ x ≤ 1/2, 1/2 ≤ x.

call them A B and C.

So A or B or C.

If A, the equation is true if (say) a.

If B, the equation is true if (say) b.

If C, the equation is true if (say) c.

So the equation is true if (A and a) or (B and b) or (C and c).