"Write an algebraic expression that uses x, y, and z and simplifies to 16 when x=-3, y=-2, and z=-1.Use only multiplication and division." And please explain!!!
well, xyz = -6
so, -8xyz/3 = 16
To create an algebraic expression that simplifies to 16 when x=-3, y=-2, and z=-1 using only multiplication and division, we can proceed as follows:
Step 1: Start with the expression "x * y * z". This represents the multiplication of the variables x, y, and z.
Step 2: Substitute the given values of x, y, and z into the expression: "(-3) * (-2) * (-1)".
Step 3: Simplify the expression:
(-3) * (-2) = 6
6 * (-1) = -6
So, the simplified expression that equals 16 when x=-3, y=-2, and z=-1 is "-6".
Explanation:
We begin by setting up the expression "x * y * z" since we want to use the variables x, y, and z. Then, we substitute the given values of x, y, and z into the expression. The negatives in front of the numbers represent the given values, as indicated by "x=-3, y=-2, and z=-1". Finally, we simplify the expression by performing the multiplication operation, which results in "-6". This is the algebraic expression that simplifies to 16 when the given values are plugged in for x, y, and z.
To create an algebraic expression that simplifies to 16 when x = -3, y = -2, and z = -1 using only multiplication and division, we need to break down the problem into smaller steps.
Step 1: Give variables to the values x, y, and z.
Let's assign the variables a, b, and c to the values x, y, and z, respectively. Therefore, a = -3, b = -2, and c = -1.
Step 2: Determine the relationship between these variables.
Since we need the expression to simplify to 16, we can deduce that the expression will involve multiplication and division between a, b, and c.
Step 3: Create the algebraic expression.
Let's construct the expression step by step.
- First, let's create a denominator involving a and b, as we will be performing division. Since we want a final value of 16 when x = -3 and y = -2, we can use the expression (a - b) as the denominator.
- Next, let's consider the numerator, which will involve the variables a, b, and c to reach the desired value of 16.
- We know that x = -3 (a = -3), y = -2 (b = -2), and z = -1 (c = -1). The expression (a * b * c) will give us positive 6 in this case.
- To simplify further, we need to find a factor that, when divided by (a - b), gives us the desired answer of 16.
- After some calculations, we find that multiplying the numerator by 8 will give us the desired value of 16 (6 * 8 = 48, then dividing by (a - b) gives us 16).
Combining all these steps, the algebraic expression that satisfies the conditions is:
(8 * (a * b * c)) / (a - b)
Substituting a = -3 and b = -2:
(8 * (-3 * -2 * -1)) / (-3 - (-2))
(8 * 6) / (-3 + 2)
Simplifying further:
48 / (-1)
-48
Therefore, when x = -3, y = -2, and z = -1, the algebraic expression (8 * (a * b * c)) / (a - b) simplifies to -48, not 16.