Another Question "-_- (1 Viewer)

[scardizzle]

|2x - 1| < / = |x -3|

This is another novincial thing I've forgotten how to do.

i took the case where both sides are positive which gives me x >/= -2

then i took the case where both sides are negative which gives me the same answer

but what about when one side is negative and the other side is positive?

I get the same answer for both cases but the inequality sign

e.g. when LHS is positive and RHS is negative i get x </= 4/3

when LHS is negative and RHS is positive i get x >/= 4/3

which result is correct?

 

[mchew92]

Case 1:
the LHS becomes (2x-1)
Case 2:
the LHS becomes -(2x-1)

the RHS doesnt really change
N.B- if it is not an inequlity, u must check your answer by subbing in value.

 

[MSELIM2]

im not sure if im right but i got x to be 1/2

 

[Timothy.Siu]

wheres the question?

 

[gurmies]

|2x-1| <= |x-3|

Solve for |2x-1| = |x-3|

2x-1 = x-3 OR/ 2x-1 = -x+3

x = -2 OR/ x = 4/3

Test between points (e.g. x = 0)

|-1| <= |-3| which is true.

.'. -2 <= x <= 4/3

You can also test x > 4/3 and x < -2 but I know those will not satisfy the inequality.

 

[scardizzle]

wheres the question?

yeh sorry fixed now didnt realize "< /" makes the text after it disappear (damn forum code)

|2x-1| <= |x-3|

Solve for |2x-1| = |x-3|

2x-1 = x-3 OR/ 2x-1 = -x+3

x = -2 OR/ x = 4/3

Test between points (e.g. x = 0)

|-1| <= |-3| which is true.

.'. -2 <= x <= 4/3

You can also test x > 4/3 and x < -2 but I know those will not satisfy the inequality.

+1

 

[untouchablecuz]

|2x-1| <= |x-3|

sqrt[(2x-1)^2] <= sqrt[(x-3)^2]

(2x-1)^2 <= (x-3)^2

4x^2-4x+1<=x^2-6x+9

3x^2+2x-8<=0

3x^2+6x-4x-8<=0

3x(x+2)-4(x+2)<=0

(3x-4)(x+2)<=0

-2<=x<=4/3

 

[khorne]

While |a| = |b| ( -a = b, -a = -b, a = -b, a = b) technically has 4 solutions, 2 of them will always be repeats of the other 2...

 

[Trebla]

As sorta highlighted by untouchablecuz, since both sides of the inequality are positive, you can just square both sides and solve it like a quadratic inequality. No need to worry about cases (which are really annoying). Remember that squaring both sides is only problematic when one side of inequality could be negative. If both sides are positive, squaring both sides preserves the sign of the inequality.