Answer:
a) x = 3
b) x = 10/9
c) x = -1/13
d) x = 13/6
Step-by-step explanation:
To solve in an easy way each equation is convenient to multiply the equation by the m.c.m, in order to eliminate the denominators. Next you sum terms with x and coefficients to obtain x:
a)
m.c.m = 3
[tex]\frac{5}{3}x-3+x=2x-1\\\\(\frac{5}{3}x-3+x=2x-1)*3\\\\5x-9+3x=6x-3\\\\5x+3x-6x=-3+9\\\\2x=6\\\\x=\frac{6}{2}=3[/tex]
b)
m.c.m = 4
[tex]3x+2x-\frac{1}{2}=5+x-\frac{2}{4}\\\\(3x+2x-\frac{1}{2}=5+x-\frac{2}{4})*4\\\\12x+8x-2=20+2x-2\\\\12x+8x-2x=20-2+2\\\\18x=20\\\\x=\frac{20}{18}=\frac{10}{9}[/tex]
c)
m.c.m = 6
[tex]\frac{x}{2}-2x-\frac{1}{3}=3x-\frac{x}{6}\\\\(\frac{x}{2}-2x-\frac{1}{3}=3x-\frac{x}{6})*6\\\\3x-12x-2=18x-x\\\\3x-12x-18x+x=2\\\\-26x=2\\\\x=-\frac{2}{26}=-\frac{1}{13}[/tex]
d)
m.c.m = 6
[tex]x+\frac{2}{3}-4x-1=2-4x-\frac{1}{6}\\\\(x+\frac{2}{3}-4x-1=2-4x-\frac{1}{6})*6\\\\6x+4-24x-6=12-24x-1\\\\6x-24x+24x=12-1-4+6\\\\6x=13\\\\x=\frac{13}{6}[/tex]
