[tex] \frac{2}{3} x + \frac{1}{6} = -\frac{3}{4} x + 1[/tex]
First, simplify [tex] \frac{2}{3} x[/tex] to [tex] \frac{2x}{3} [/tex] / Your problem should look like: [tex] \frac{2x}{3} + \frac{1}{6} = -\frac{3}{4} x + 1[/tex]
Second, simplify [tex] \frac{3}{4} x[/tex] to [tex] \frac{3x}{4} [/tex] / Your problem should look like: [tex] \frac{2x}{3} + \frac{1}{6} = -\frac{3x}{4} + 1[/tex]
Third, multiply both sides by 12 (the LCM of 3 and 4) / Your problem should look like: [tex]8x + 2 = -9x + 12[/tex]
Fourth, subtract 2 from both sides. / Your problem should look like: [tex]8x = -9x + 12 - 2[/tex]
Fifth, simplify -9x + 12 - 2 to -9x + 10. / Your problem should look like: [tex]8x = -9x + 10[/tex]
Sixth, add 9x to both sides. / Your problem should look like: [tex]8x + 9x = 10[/tex]
Seventh, add 8x + 9x to get 17x. / Your problem should look like: [tex]17x = 10[/tex]
Eighth, divide both sides by 17. / Your problem should look like: [tex]x = \frac{10}{17} [/tex]
Answer as fraction: x = [tex] \frac{10}{17} [/tex]
Answer as decimal: x = 0.5882
