solve the equation.\n\\( \\frac { 3 } { 4 } x + 3 - 2 x = - \\frac { 1 } { 4 } + \\frac { 1 } { 2 } x + 5 \\)

Explanation:

Step1: Combine like terms on both sides

Combine ( \frac{3}{4}x - 2x) on the left - hand side: (\frac{3}{4}x-2x=\frac{3}{4}x-\frac{8}{4}x=-\frac{5}{4}x). Combine (-\frac{1}{4}+5) on the right - hand side: (-\frac{1}{4}+5=\frac{-1 + 20}{4}=\frac{19}{4}). The equation becomes (-\frac{5}{4}x+3=\frac{1}{2}x+\frac{19}{4}).

Step2: Get all (x) terms on one side

Subtract (\frac{1}{2}x) from both sides. (-\frac{5}{4}x-\frac{1}{2}x+3=\frac{1}{2}x-\frac{1}{2}x+\frac{19}{4}). Since (-\frac{1}{2}x=-\frac{2}{4}x), then (-\frac{5}{4}x-\frac{2}{4}x+3=\frac{19}{4}), (-\frac{7}{4}x + 3=\frac{19}{4}).

Step3: Get the constant terms on one side

Subtract 3 from both sides. (-\frac{7}{4}x+3 - 3=\frac{19}{4}-3). Since (3=\frac{12}{4}), then (-\frac{7}{4}x=\frac{19}{4}-\frac{12}{4}), (-\frac{7}{4}x=\frac{7}{4}).

Step4: Solve for (x)

Multiply both sides by (-\frac{4}{7}). (x=\frac{7}{4}\times(-\frac{4}{7})).

Answer:

(x=-1)