Sign In
Break down the given absolute value equation two separate equations.
p=10 and p=2/3
When solving an equation involving absolute value expressions, we should consider what would happen if we removed the absolute value symbols. Let's look at an example equation. |ax+b|=|cx+d| Although we can make 4 statements about this equation, there are actually only two possible cases to consider.
Statement | Result |
---|---|
Both absolute values are positive. | ax+b=cx+d |
Both absolute values are negative. | -(ax+b)=-(cx+d) |
Only the left-hand side is negative. | -(ax+b)=cx+d |
Only the right-hand side is negative. | ax+b=-(cx+d) |
lc 4(p-3) ≥ 0:4(p-3) = (2p+8) & (I) 4(p-3) < 0:4(p-3) = - (2p+8) & (II)
(I):Distribute 4
(II):Distribute 4 & -1
(I), (II):LHS+12=RHS+12
(I):LHS-2p=RHS-2p
(I):.LHS /2.=.RHS /2.
(II):LHS+2p=RHS+2p
(II):.LHS /6.=.RHS /6.
(II):a/b=.a /2./.b /2.
p= 10
Multiply
Add and subtract terms
|7|=7
Multiply
|28|=28
p= 2/3
a*b/c= a* b/c
Rewrite 3 as 9/3
Rewrite 8 as 24/3
Add and subtract fractions
|-7/3|=7/3
a*b/c= a* b/c
|28/3|=28/3