Question

What number must be placed in the box in the equation below to produce an equation that has more than one solution: 5u+3(4u-6)=-3u-27+20u+ ▢

Answer 1

Answer: the number must be placed in the box is 9

suppose: the number must be placed in the box is x

have:

5u + 3(4u - 6) = -3u -27 + 20u + x

⇔ 5u + 12u - 18 = -3u - 27 + 20u +x

⇔ 17u + 3u - 20u = -27 + 18 + x

⇔ 0 = x - 9

⇔ x = 9

Explanation:

Answer 2

9

Explanation:

Simplifying both sides gives

17u - 18 = 17u - 27 + ▢.

Subtracting 17u from both sides gives

-18 = -27 + ▢.

If the number in the box is anything but 9, then the equation cannot be true, and the original equation has no solutions. If the number in the box is 9, then the two sides of the original equation are equivalent, and all values of u are solutions to the equation.