what is the solution to the linear equation?\n\\( \\frac { 2 } { 3 } x - \\frac { 1 } { 2 } = \\frac { 1 } {…

what is the solution to the linear equation?\n\\( \\frac { 2 } { 3 } x - \\frac { 1 } { 2 } = \\frac { 1 } { 3 } + \\frac { 5 } { 6 } x \\)\n\\( x = - 5 \\)\n\\( x = - \\frac { 1 } { 6 } \\)\n\\( x = \\frac { 1 } { 6 } \\)\n\\( x = 5 \\)

what is the solution to the linear equation?\n\\( \\frac { 2 } { 3 } x - \\frac { 1 } { 2 } = \\frac { 1 } { 3 } + \\frac { 5 } { 6 } x \\)\n\\( x = - 5 \\)\n\\( x = - \\frac { 1 } { 6 } \\)\n\\( x = \\frac { 1 } { 6 } \\)\n\\( x = 5 \\)

Answer

Explanation:

Step1: Eliminate the denominators

Multiply each term by (6) (the least common multiple of (2), (3), and (6)): (6\times\frac{2}{3}x - 6\times\frac{1}{2}=6\times\frac{1}{3}+6\times\frac{5}{6}x) (4x - 3 = 2+5x)

Step2: Isolate the variable (x)

Subtract (4x) from both sides: (4x - 3-4x=2 + 5x-4x) (-3=2+x) Subtract (2) from both sides: (-3 - 2=2+x - 2) (-5=x)

Answer:

(x = - 5) (the first option)