Answer:
No solution for [tex]\frac{1}{4}(x-3)=3x-\frac{11}{4}x-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.
1. We simplify any parenthesis. We multiply by 1/4 on the left side.
[tex]\frac{1}{4} (x-3)=3x-\frac{11}{4}x-3\\\frac{1}{4}x-\frac{1}{4}(3)=3x-\frac{11}{4}x-3[/tex]
[tex]\frac{1}{4}x-\frac{3}{4} =3x-\frac{11}{4}x-3[/tex]
2. We undo any subtraction or addition by doing the inverse on both sides.
[tex]\frac{1}{4} x-\frac{3}{4} +\frac{3}{4}=3x-\frac{11}{4}x-3+\frac{3}{4}\\\frac{1}{4} x=3x-\frac{11}{4}x-\frac{9}{4}[/tex]
3. Add like terms for x on the right side then subtract from both sides.
[tex]\frac{1}{4} x=\frac{1}{4}x-\frac{9}{4}\\\frac{1}{4} x-\frac{1}{4}x=\frac{1}{4}x-\frac{1}{4}x-\frac{9}{4}\\0x=0x-\frac{9}{4}\\0\neq- \frac{9}{4}[/tex]
Our answer is no solution because no variable remains and the equation is false.
