Solve each equation.
1. (|3x -4|)/(-5) = 6
A: no solution
2. (|2x -5|) = x + 3
A: x = 8 or x = 2/3
Solve each inequality.
3. |5x + 15| > 20
A: x > 1 and x < -7
4. [(|x - 2|)/ (4) greater than or equal to 5
A: -18 < x < 22
5. (-3) x (|5x - 8|)- 5 greater than or equal to 6
A: no solution?
6. |12 - 4x| - 4 > 20
A: x < -3 and x > 9
1. (|3x -4|)/(-5) = 6
(|3x -4|) = -30
or
3x-6 = -30
or
-3x+6 = -30
so
x = -24/3 = -8
or
x = 12
2. (|2x -5|) = x + 3
A: x = 8 or x = 2/3
=========================
2x-5 = x+3
or
-2x+5 = x+3
x = 8
or
x = 2/3 you got that right. Why did you miss #1 ????
3. |5x + 15| > 20
A: x > 1 and x < -7
5x +15 > 20
or
-5x - 15 >20
x > 1 yes
-5x > -35
divide both sides by -5 and reverse the arrow
x < 7 why the sign ?????
4. [(|x - 2|)/ (4) greater than or equal to 5
A: -18 < x < 22
===========================
x-2 >/=20
or
-x+2 >/= 20
x >/= 22
x </= -18
1. How did 4 suddenly become 6?
5. (-3) x (|5x - 8|)- 5 greater than or equal to 6
A: no solution?
============================
3 (-3) x (|5x - 8|)- 5 >/= 6
(-3) x (|5x - 8|) >/= 11
x (|5x-8)| </= -11/3
x(5x-8) </= -11/3
x(-5x+8) </= -11/33
5 x^2 - 8 x </= -11/3
-5 x^2 + 8 x </= -11/3
graph 5 x^2 - 8 x + 11/3 = 0
No real solution
1. (|3x -4|)/(-5) = 6
(|3x -4|) = -30
or
3x-4 = -30
or
-3x+4 = -30
so
x = -26/3
or
x = 34/3
6. |12 - 4x| - 4 > 20
A: x < -3 and x > 9
============================
12 -4 x > 24
or
-12 + 4x >24
-4x > 12
or
4x > 36
x < -3
or
x > 9
Will you explain to me why there is a solution to #1?
1. (|3x -4|)/(-5) = 6
A: no solution
=========================
multiply both sides by - 5 , no arrow business because just an equal sign
3 x - 4 = -30
or
-3x + 4 = -30
3 x = -26
or
-3x = -34
so there are two solutions