8y+4=2|y-1|
ive been working at this problem but i cant solve it....plz help me
8y+4=2|y-1|
Divide both sides by 2:
4y+2=|y-1|
Split into two equations to get rid of absolute value:
-(4y+2)=y-1 and (4y+2)=y-1
Solve for y:
-4y-2=y-1 4y+2=y-1
-4y-1=y 4y=y-3
-1=5y 3y=-3
-1/5=y y=-1
Plug both solutions into original equation and solve:
y=-1/5 y=-1
8(-1/5)+4=2|(-1/5)-1| 8(-1)+4=2|(-1)-1|
4(-1/5)+2=|-1/5-1| 4(-1)+2=|-1-1|
-4/5+10/5=|-1/5-5/5| -4+2=|-2|
6/5=|-6/5| -2=|-2|
6/5=6/5 -2=2
Since 6/5=6/5 is a true statement, y=-1/5 is a solution.
Since -2=2 is NOT a true statement, y=-1 is NOT a solution.
Therefore, the answer is y=-1/5.
I'll give it a shot, thx u so much
it didnt work....im not good at math
oh wait i think it works!
To solve this equation, we will need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: When y - 1 is positive (y > 1)
In this case, the equation can be rewritten without the absolute value:
8y + 4 = 2(y - 1)
Solve for y:
8y + 4 = 2y - 2
Subtract 2y from both sides:
6y + 4 = -2
Subtract 4 from both sides:
6y = -6
Divide both sides by 6:
y = -1
Case 2: When y - 1 is negative (y < 1)
In this case, the equation can also be rewritten without the absolute value:
8y + 4 = 2(-y + 1)
Solve for y:
8y + 4 = -2y + 2
Add 2y to both sides:
10y + 4 = 2
Subtract 4 from both sides:
10y = -2
Divide both sides by 10:
y = -0.2
Therefore, the solutions to the equation are y = -1 and y = -0.2.