I 2x - 9/2 I = I 7 - 3x I
The "I" is for absolute value. Solve algebraically and write answer in a solution set.
Where do I start???
That is an absolute value question.
Okay, if you have absolute value on both sides of the equation...
2x - 9/2 = 7 - 3x or 2x - 9/2 = -( 7 - 3x ) <<you negated this one because l a l = a or -a
let's take the equation on the left first.
2x - 9/2 = 7 - 3x
5x = 7 + 9/2 solving for x
5x = 23/2 added the fractions
x = [23/2]/5 divided both sides by 5
x = 23/10 <<this is your first solution.
Now, let's take the other equation.
2x - 9/2 = -( 7 - 3x )
2x - 9/2 = -7 + 3x
-x = -7 + 9/2
-x = -5/2
x = 5/2
Therefore, the solution set is {23/10,5/2}
Hi,
Make 2 equations - one with the expression set equal to each other without absolute vale bars, and then write a second equation with one expression equal to the opposite of the second expression. Then solve both equations.
Multiply by 2.
4x - 9 = 14 - 6x
10x = 23
x = 2 3/10 <==ANSWER
-x - 9/2 = -7
x = 5/2 <==ANSWER
I hope that helps!! :-)
this gives 2 equations:
A. 2x-9/2=7-3x and B. 2x-9/2=-(7-3x)
Solve each of these, and CHECK EACH SOLUTION.
A). 2X-9/2=7-3X 2X-9/2=-7+3X
5X=7+9/2 -1X=-7+9/2
5X=11 1/2 -1X=-5/2
X=23/10 X=5/2
Solution set: X = {23/10, 5/2}
so (I 2x - 9/2 I)^2 = (I 7 - 3x I)^2
so (2x-9/2)^2=(7-3x)^2
4x^2+ 81/4 -18x=49+9x^2-42x
multiply both sides by 4
16x^2+81-72x=196+36x^2-168x
- 20x^2+96x-115=0
using the quadratic formula:
delta=96^2-4*(-115)*(-20)=16
x=(-96-sqrt(16))/(-40) OR x=(-96+sqrt(16))/(-40)
so x= 5/2 OR x= 23/10
just remember (IxI)^2=(x)^2 because (x)^2=(-x)^2
2x - 9/2 = 7 - 3x add 3x and 9/2 to both sides.
5x = 23/2 now divide both sides by 5
x = (23/2)/5 = 23/2*5
x = 23/10
Comments
That is an absolute value question.
Okay, if you have absolute value on both sides of the equation...
I 2x - 9/2 I = I 7 - 3x I
2x - 9/2 = 7 - 3x or 2x - 9/2 = -( 7 - 3x ) <<you negated this one because l a l = a or -a
let's take the equation on the left first.
2x - 9/2 = 7 - 3x
5x = 7 + 9/2 solving for x
5x = 23/2 added the fractions
x = [23/2]/5 divided both sides by 5
x = 23/10 <<this is your first solution.
Now, let's take the other equation.
2x - 9/2 = -( 7 - 3x )
2x - 9/2 = -7 + 3x
-x = -7 + 9/2
-x = -5/2
x = 5/2
Therefore, the solution set is {23/10,5/2}
Hi,
I 2x - 9/2 I = I 7 - 3x I
Make 2 equations - one with the expression set equal to each other without absolute vale bars, and then write a second equation with one expression equal to the opposite of the second expression. Then solve both equations.
2x - 9/2 = 7 - 3x
Multiply by 2.
4x - 9 = 14 - 6x
10x = 23
x = 2 3/10 <==ANSWER
2x - 9/2 = -7 + 3x
-x - 9/2 = -7
-x = -5/2
x = 5/2 <==ANSWER
I hope that helps!! :-)
this gives 2 equations:
A. 2x-9/2=7-3x and B. 2x-9/2=-(7-3x)
Solve each of these, and CHECK EACH SOLUTION.
A). 2X-9/2=7-3X
2X-9/2=-7+3X
5X=7+9/2 -1X=-7+9/2
5X=11 1/2 -1X=-5/2
X=23/10 X=5/2
Solution set: X = {23/10, 5/2}
I 2x - 9/2 I = I 7 - 3x I
so (I 2x - 9/2 I)^2 = (I 7 - 3x I)^2
so (2x-9/2)^2=(7-3x)^2
4x^2+ 81/4 -18x=49+9x^2-42x
multiply both sides by 4
16x^2+81-72x=196+36x^2-168x
- 20x^2+96x-115=0
using the quadratic formula:
delta=96^2-4*(-115)*(-20)=16
x=(-96-sqrt(16))/(-40) OR x=(-96+sqrt(16))/(-40)
so x= 5/2 OR x= 23/10
just remember (IxI)^2=(x)^2 because (x)^2=(-x)^2
2x - 9/2 = 7 - 3x add 3x and 9/2 to both sides.
5x = 23/2 now divide both sides by 5
x = (23/2)/5 = 23/2*5
x = 23/10