Answer:
The equation has a real solution which is:
[tex]x=\frac{11}{16}[/tex]
Step-by-step explanation:
Given the equation
[tex]2x+\frac{1}{4}=4x-\frac{9}{8}[/tex]
Solving the equation
[tex]2x+\frac{1}{4}=4x-\frac{9}{8}[/tex]
Subtract 1/4 from both sides
[tex]2x+\frac{1}{4}-\frac{1}{4}=4x-\frac{9}{8}-\frac{1}{4}[/tex]
Simplify
[tex]2x=4x-\frac{11}{8}[/tex]
Subtract 4x from both sides
[tex]2x-4x=4x-\frac{11}{8}-4x[/tex]
Simplify
[tex]-2x=-\frac{11}{8}[/tex]
Divide both sides by -2
[tex]\frac{-2x}{-2}=\frac{-\frac{11}{8}}{-2}[/tex]
Simplify
[tex]x=\frac{11}{16}[/tex]
Therefore, the equation has a real solution which is:
[tex]x=\frac{11}{16}[/tex]
