Just translate the words into math. Let x be the number you're looking for The additive inverse of a number ---- -x divided by 12 ---- -x/12 is the same as ---- -x/12 1 less than 3 times its reciprocal ---- -x/12 3/x - 1 Now you have something that you can solve -x 36/x - 12 -x + 12 36/x -x^2 + 12x - 36 0 I'm not good at factoring, so I usually resort to the quadratic formula which, in this case, shows both roots to be 6 Check: -x/12 3/x - 1 -6/12 3/6 - 1 -1/2 1/2 - 1 -1/2 -1/2 Check!
Let x be the number for which you are looking. The additive inverse is -x. The reciprocal is (1 / x) (-x / 12) 3 * (1/x) - 1 Multiply both sides of this equation by the least common denominator which is 12x, getting:: -x^2 12 * (3) - 12x Since, when I'm factoring. I like the x^2 term to be positive, multiply both sides by (-1), getting: x^2 12x - 36Subtract 12x - 36 from both sides x^2 - 12x - (-36) 0 x^2 - 12x + 36 0 (x - 6)^2 0 6Answer Note: In the rush of a test it's better to factor nice quadratic equations than to deal with the quadratic formula. Just make sure everything is on the left hand side of the equation and that the x^2 term is positive before you factor. Checking: -6/12 ? (3 / (6)) - 1 -1/2 ? (1/2) - 1 -1/2 ? -1/2.Yes it does so the answer is correct. .
