Start with
[tex]\dfrac{5-2x}{3}+1-\dfrac{3x-2}{5}=-x[/tex]
Multiply both sides by 15 to get rid of denominators:
[tex]5(5-2x)+15-3(3x-2)=-15x[/tex]
Expand the left hand side:
[tex]25-10x+15-9x+6=-15x[/tex]
Move all terms involving x to the left and all numbers to the right:
[tex]-10x-9x+15x=-25-15-6[/tex]
Sum like terms:
[tex]-4x=-46[/tex]
Divide both sides by -4:
[tex]x=\dfrac{46}{4}=\dfrac{23}{3}[/tex]
