Please check if I did this right...
√(2x+1)+7= 3
-7 -7
√(2x+1)= -4
Square everything
√(2x+1)^2= -4^2
2x+1=16
-1 -1
2x=15
divide by 2 on both sides
x=7.5
CHECK: (Plug it in)
√(2(7.5)+1)+7= 3
√(16)+7= 3
4+7=3
11 doesn't equal 3
so the answer is no solution? right?
correct, no solution
Thank you so much!
Yes, you have correctly solved the equation up until the step where you obtained 2x = 15. However, when you divided both sides by 2 to solve for x, you made an arithmetic error. Dividing 15 by 2 gives you x = 7.5, not x = 7.
Let me go through the steps to solve the equation and check if you did it right:
1. Start with the equation: √(2x + 1) + 7 = 3
2. Subtract 7 from both sides: √(2x + 1) = -4
3. Square both sides of the equation to eliminate the square root: (√(2x + 1))^2 = (-4)^2
4. Simplify: 2x + 1 = 16
5. Subtract 1 from both sides: 2x = 15
6. Divide both sides by 2: x = 7.5
Now, let's check if the solution is correct by plugging it back into the original equation:
√(2(7.5) + 1) + 7 = 3
√(15 + 1) + 7 = 3
√16 + 7 = 3
4 + 7 = 3
11 = 3
Since 11 does not equal 3, we can conclude that there is no solution to the original equation.