Question

(½) (6x + 3) = 7 – (3x + 1)

Answer 1

`\tt Step-by-step~explanation:`

To solve for x, we have to remember to isolate the variable.

`\tt Step~1:`

For 1/2, we can make that 0.5, since their values are equivalent. Our equation:

`\tt (0.5)(6x+3)=7-(3x+1)`

Let's distribute the 0.5 first.

`\tt 0.5*6x=3x\\0.5*3=1.5`

`\tt Step~2:`

Now, let's simplify the right side of the equation. We have to distribute the negative to 3x and 1.

`\tt -1*3x=-3x\\-1*1=-1`

Then, we simplify the entire expression.

`\tt 7-3x-1=-3x+6`

`\tt Step~3:`

Our equation now:

`\tt 3x+1.5=-3x+6`

Let's add 3x to the right and 3x to the left to simplify the -3x on the right side of the equation.

`\tt 3x(+3x)+1.5=-3x (3x)+6\\6x+1.5=6`

`\tt Step~4:`

Let's do the same thing we did in Step 3 to 1.5. Subtract 1.5 on both sides of the equation.

`\tt 6x+1.5(-1.5)=6(-1.5)\\6x=4.5`

`\tt Step~5:`

Finally, we divide both sides by 6 to isolate x.

`\tt (6x)/(6) =x\\(4.5)/(6)= 0.75~or~(3)/(4)`

`\large\boxed{\tt Our~final~answer:~x=0.75~(or~(3)/(4))}`