[tex]\tt Step-by-step~explanation:[/tex]
To solve for x, we have to remember to isolate the variable.
[tex]\tt Step~1:[/tex]
For 1/2, we can make that 0.5, since their values are equivalent. Our equation:
[tex]\tt (0.5)(6x+3)=7-(3x+1)[/tex]
Let's distribute the 0.5 first.
[tex]\tt 0.5*6x=3x\\0.5*3=1.5[/tex]
[tex]\tt Step~2:[/tex]
Now, let's simplify the right side of the equation. We have to distribute the negative to 3x and 1.
[tex]\tt -1*3x=-3x\\-1*1=-1[/tex]
Then, we simplify the entire expression.
[tex]\tt 7-3x-1=-3x+6[/tex]
[tex]\tt Step~3:[/tex]
Our equation now:
[tex]\tt 3x+1.5=-3x+6[/tex]
Let's add 3x to the right and 3x to the left to simplify the -3x on the right side of the equation.
[tex]\tt 3x(+3x)+1.5=-3x (3x)+6\\6x+1.5=6[/tex]
[tex]\tt Step~4:[/tex]
Let's do the same thing we did in Step 3 to 1.5. Subtract 1.5 on both sides of the equation.
[tex]\tt 6x+1.5(-1.5)=6(-1.5)\\6x=4.5[/tex]
[tex]\tt Step~5:[/tex]
Finally, we divide both sides by 6 to isolate x.
[tex]\tt \frac{6x}{6} =x\\\frac{4.5}{6}= 0.75~or~\frac{3}{4}[/tex]
[tex]\large\boxed{\tt Our~final~answer:~x=0.75~(or~\frac{3}{4})}[/tex]