Question

PLEASE ANSWER BRANILEST AND 50 POINTSSSS!

Answer 1

`\[4(x + 3) - 4 = 8\left((1)/(2)x + 1\right)\]`

Explanation:

To set up an equation with infinite solutions, the coefficients of x on both sides need to be equal. Let's manipulate the given equation:


`\[4(x + 3) - 4 = y\left((1)/(2)x + 1\right)\]`

Distribute on both sides:


`\[4x + 12 - 4 = (y)/(2)x + y\]`

Combine like terms:


`\[4x + 8 = (y)/(2)x + y\]`

To make the coefficients of x equal, we can multiply both sides by 2:


`\[8x + 16 = yx + 2y\]`

Now, subtract
`(yx + 2y\)`) from both sides:


`\[8x + 16 - yx - 2y = 0\]`

Combine like terms:


`\[(8 - y)x + (16 - 2y) = 0\]`

For infinite solutions, set both coefficients equal to zero:


`\[8 - y = 0 \quad \text{and} \quad 16 - 2y = 0\]`

Solve these equations simultaneously:


`\[y = 8 \quad \text{and} \quad y = 8\]`

So, if
`y = 8` the equation has infinite solutions. The completed equation is:


`\[4(x + 3) - 4 = 8\left((1)/(2)x + 1\right)\]`