Question

The expression on the left side of an equation is shown below.

3 (x + 1) + 9 = box

If the equation has no solution, which expression can be written in the box on the other side of the equation?
3 (x + 4)
2 (x + 6) + x
4(x – 3) – x
3 (x + 1) + 9 x

Answer 1

(c) 4(x -3) -x

Explanation:

You want an expression for the right side of the equation that will ensure the equation has no solutions.

No solution

The equation will have no solution when it is of the form ...

ax +b = ax +c . . . . . . where b ≠ c

The given expression simplifies to ...

3(x +1) +9 = 3x +3 +9 = 3x +12

The desired expression must have an x-coefficient of 3 and a different constant than +12.

Choices

(a) 3(x +4) = 3x +12 . . . . . . infinitely many solutions

(b) 2(x +6) +x = 3x +12 . . . . infinitely many solutions

(c) 4(x -3) -x = 3x -12 . . . . . no solutions

(d) 3(x +1) +9x = 12x +3 . . . . one solution

__

Additional comment

When the equation is of the form 3x +12 = 3x +12, any value of x will satisfy the equation. It has infinitely many solutions.

The solution to (d) 3x +12 = 12x +3 is x = 1, one solution.

<95141404393>