Question

Please help asap. Making this 50 points!

Answer 1

The missing number is 14.

Explanation:

Given equation:

let space be a.

`\sf \sf 2(4x + 12) = 2(-3x - 10) + ax + 10`

Distribute the constants on both sides:

`\sf 8x + 24 = -6x - 20 + ax + 10`

Combine like terms:

`\sf 8x + 24 = (-6 + a)x - 10`

Now, to have no solutions, the coefficient of x on the left side (-6 + a) must be the same as the coefficient of x on the right side (8).

In other words, we want a situation where the value of x will make these coefficients equal.

This can be achieved if:

`\sf -6 + a = 8`

Solve for "a":

`\sf a = 8 + 6`

`\sf a = 14`

Therefore, for the equation to have no solutions, the value of "a" should be 14.

So, The Final answer is:

`\sf 2(4x + 12) = 2(-3x - 10) + \boxed{\sf 14}x + 10`