Answer:
x = -1
Step-by-step explanation:
The usual approach to these is to square the radicals until they are gone.
![\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csqrt%7B3x%2B7%7D%2B%5Csqrt%7Bx%2B1%7D%3D2%5C%5C%5C%5C%283x%2B7%29%20%2B2%5Csqrt%7B%283x%2B7%29%28x%2B1%29%7D%2B%28x%2B1%29%20%3D%204%5Cqquad%5Ctext%7Bsquare%20both%20sides%7D%5C%5C%5C%5C2%5Csqrt%7B%283x%2B7%29%28x%2B1%29%7D%3D-4x-4%5Cqquad%5Ctext%7Bsubtract%20%244x%2B8%24%7D%5C%5C%5C%5C%283x%2B7%29%28x%2B1%29%3D%28-2x-2%29%5E2%5Cqquad%5Ctext%7Bdivide%20by%202%2C%20square%20again%7D%5C%5C%5C%5C3x%5E2%2B10x%20%2B7%3D4x%5E2%2B8x%2B4%5Cqquad%5Ctext%7Bsimplify%7D%5C%5C%5C%5Cx%5E2-2x-3%3D0%5Cqquad%5Ctext%7Bsubtract%20the%20left%20expression%7D%5C%5C%5C%5C%28x-3%29%28x%2B1%29%3D0%5Cqquad%5Ctext%7Bfactor%7D%5C%5C%5C%5Cx%3D3%2C%5C%20x%3D-1%5Cqquad%5Ctext%7Bsolutions%20to%20the%20quadratic%7D)
Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.
The solution is x = -1.
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Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.
Answer:
0.28142
Step-by-step explanation:
Hope this helps you
One of the numbers are negative
Remember this... a negative divided by a positive will result in a negative and a negative divided by a negative will result in a positive, the same goes for multiplication
Answer:
![\frac{7}{10} y](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B10%7D%20y)
Step-by-step explanation:
To add fractions <em>with the same denominator</em>, simply add the numerators:
![\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D%20%2B%20%5Cfrac%7Bc%7D%7Bb%7D%20%3D%20%5Cfrac%7Ba%2Bc%7D%7Bb%7D)
So:
![\frac{3}{10} y+\frac{4}{10} y=\frac{7}{10} y](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B10%7D%20y%2B%5Cfrac%7B4%7D%7B10%7D%20y%3D%5Cfrac%7B7%7D%7B10%7D%20y)
Answer:
3200
Step-by-step explanation: