Solve the equation (3x+1)^2=16 by the Square Root Method.
So did I do this right:
1) (√3x+1) = (√16)
2) 3x+1=4 (because the √16= 4)
3) 3x+1-1=4-1
4) 3x=3
5) 3x/3=3/3
6) x= 1 (because 3/3=1)
actually, if
(3x+1)^2=16
then 3x+1 = ± 4
3x+1 = 4 or 3x+1 = -4
3x = 3 or 3x = -5
x = 1 or x = -5/3
Thank you reiny
(3x+1)^2=16
(3x+1)^2 = 4^2
so
3x + 1 = 4
3x = 3
x = 1
of course also
(3x+1)^2=16
(3x+1)^2= (-4)^2 = 16 just like (+4)^2 = 16
3x+ 1 = -4
3x = -5
x = -5/3
To solve the equation (3x+1)^2=16 using the Square Root Method, follow these steps:
Step 1: Rewrite the equation in the form (3x+1)^2 = (√16)^2.
Step 2: Take the square root of both sides of the equation to eliminate the square exponent. Remember that when taking the square root, you need to consider both the positive and negative roots.
√[(3x+1)^2] = ±√(16).
Step 3: Simplify the equation by removing the square root:
3x+1 = ±4.
Step 4: Solve for x in each equation:
For the positive root:
3x+1 = 4.
Subtract 1 from both sides:
3x = 3.
Divide by 3:
x = 1.
For the negative root:
3x+1 = -4.
Subtract 1 from both sides:
3x = -5.
Divide by 3:
x = -5/3.
Therefore, the solutions to the equation (3x+1)^2 = 16 are x = 1 and x = -5/3.