Answer:
[tex]x=\frac{4}{3}[/tex]
Step-by-step explanation:
We can solve the equation by isolating x through order of operations. We use PEMDAS in reverse by undoing SADMEP or subtraction, addition, division, multiplication, exponents, and parenthesis.
[tex]\frac{5}{4}x+\frac{1}{2} =2x-\frac{1}{2}[/tex]
1. We simplify any parenthesis. Have none. So move on to the next step!
2. We undo any subtraction or addition by doing the inverse on both sides.
[tex]\frac{5}{4}x+\frac{1}{2}-\frac{1}{2} =2x-\frac{1}{2}-\frac{1}{2} \\\frac{5}{4}x =2x-1[/tex]
3. Now subtract an x term from both sides.
[tex]\frac{5}{4}x-2x =2x-2x-1\\\frac{5}{4}x -\frac{8}{4}x =-1\\-\frac{3}{4}x=-1[/tex]
4. Divide both sides by the coefficient of x.
[tex]-\frac{3}{4}x =-1\\x=-\frac{4}{3} (-1)\\x=\frac{4}{3}[/tex]
