Find the product of three consecutive even integers whose sum is 42.

**x = first integer**

x + 2 = second consecutive even integer

x + 2 = second consecutive even integer

**x + 4 = third consecutive even integer**{consecutive even integers increase by 2}

x + x + 2 + x + 4 = 42 {their sum is 42}

3x + 6 = 42 {combined like terms}

3x = 36 {subtracted 6 from each side}

x = 12 {divided each side by 3}

x + 2 = 14 {substituted 12, in for x, into x + 2}

x + 4 = 16 {substituted 12, in for x, into x + 4}

**the three integers are 12, 14, and 16**

Their product

= 12 x 14 x 16 {product means multiply}

=

**2688**{multiplied}

*- Algebra House*