Answer:
[tex]\mathbf{x=\frac{1}{2}}[/tex] is the solution to the equation: [tex]4x+12-8x=-1+2x+10[/tex]
The statement is true.
Option A is correct.
Step-by-step explanation:
We need to determine if [tex]x=\frac{1}{2}[/tex] is the solution to the equation: [tex]4x+12-8x=-1+2x+10[/tex]
Solving the equation first to find value of x
[tex]4x+12-8x=-1+2x+10[/tex]
Combining like terms:
[tex]4x-8x+12=2x+10-1\\-4x+12=2x+9[/tex]
Subtracting 2x on both sides
[tex]-4x+12-2x=2x+9-2x\\-4x-2x+12=9\\-6x+12=9[/tex]
Now, subtracting 12 on both sides
[tex]-6x+12-12=9-12\\-6x=-3\\[/tex]
Divide both sides by -6
[tex]\frac{-6x}{-6}=\frac{-3}{-6}\\x=\frac{1}{2}[/tex]
So, we get [tex]\mathbf{x=\frac{1}{2}}[/tex]
Therefore we can say that [tex]\mathbf{x=\frac{1}{2}}[/tex] is the solution to the equation: [tex]4x+12-8x=-1+2x+10[/tex]
The statement is true.
Option A is correct.
