Step 1. Simplify [tex] \frac{1}{5} (x+5)[/tex] to [tex] \frac{x+5}{5} [/tex]
[tex] \frac{x+5}{5} = \frac{1}{4} (x-3)+1[/tex]
Step 2. Simplify [tex] \frac{x+5}{5} [/tex] to [tex]1+ \frac{x}{5} [/tex]
[tex]1+ \frac{x}{5} = \frac{1}{4} (x-3)+1[/tex]
Step 3. Simplify [tex] \frac{1}{4} (x-3)[/tex] to [tex] \frac{x-3}{4} [/tex]
[tex]1+ \frac{x}{5} = \frac{x-3}{4} +1[/tex]
Step 4. Cancel [tex]1[/tex] on both sides
[tex] \frac{x}{5} = \frac{x-3}{4} [/tex]
Step 5. Multiply both sides by [tex]20[/tex] (the LCM of [tex]5,4[/tex])
[tex]4x=5(x-3)[/tex]
Step 6. Expand
[tex]4x=5x-15[/tex]
Step 7. Subtract [tex]5x[/tex] from both sides
[tex]4x-5x=-15[/tex]
Step 8. Simplify [tex]4x-5x[/tex] to [tex]-x[/tex]
[tex]-x=-15[/tex]
Step 9. Multiply both sides by [tex]-1[/tex]
[tex]x=15[/tex]
Done! :) Hope this helps! :)
