solve the equation and state whether the equation has one solution, no solution, or is an identity. \n\\(…

solve the equation and state whether the equation has one solution, no solution, or is an identity. \n\\( \\frac { 1 } { 2 } ( x + 6 ) = \\frac { 1 } { 2 } x - 9 \\)

solve the equation and state whether the equation has one solution, no solution, or is an identity. \n\\( \\frac { 1 } { 2 } ( x + 6 ) = \\frac { 1 } { 2 } x - 9 \\)

Answer

Explanation:

Step1: Expand the left - hand side

Use the distributive property (a(b + c)=ab+ac). Here (a=\frac{1}{2}), (b = x), (c = 6). (\frac{1}{2}(x + 6)=\frac{1}{2}x+\frac{1}{2}\times6=\frac{1}{2}x + 3) The equation becomes (\frac{1}{2}x+3=\frac{1}{2}x - 9)

Step2: Subtract (\frac{1}{2}x) from both sides

Subtracting (\frac{1}{2}x) from the left - hand side: ((\frac{1}{2}x+3)-\frac{1}{2}x=\frac{1}{2}x-\frac{1}{2}x + 3=3) Subtracting (\frac{1}{2}x) from the right - hand side: ((\frac{1}{2}x - 9)-\frac{1}{2}x=\frac{1}{2}x-\frac{1}{2}x-9=-9) We get (3=-9)

Answer:

The equation has no solution.