Answer:
[tex]x=-8[/tex]
Step-by-step explanation:
[tex]\frac{x}2} -x=\frac{x}{4} +6[/tex]
Let's begin by getting rid of the fractions by multiplying both sides of the equation by the least common multiple of the denominators 2 & 4 (4).
[tex]4(\frac{x}2} -x)=4(\frac{x}{4} +6)[/tex]
Distribute:
[tex]\frac{4x}{2} -4x=\frac{4x}{4} +24[/tex]
Simplify:
[tex]2x-4x=x+24[/tex]
Combine like terms:
[tex]-2x=x+24[/tex]
Subtract [tex]x[/tex] from both sides of the equation:
[tex]-3x=24[/tex]
Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]-3[/tex]:
[tex]x=-\frac{24}{3}[/tex]
Simplify:
[tex]x=-8[/tex]
