Set the denominator equal to zero. 0 3x + 5
The Correct Answer and Explanation is:
To set the denominator equal to zero, we first identify the denominator expression. You provided the expression:
3x + 5
To find values of x that would make the denominator equal to zero, we follow this algebraic process:
Step-by-step:
Set the denominator equal to zero:
3x + 5 = 0
Now, solve for x.
Step 1: Subtract 5 from both sides:
3x = -5
Step 2: Divide both sides by 3:
x = -5/3
So, the correct answer is:
x = -5/3
Explanation
When working with rational expressions or algebraic fractions, it’s important to understand that the denominator of a fraction can never be equal to zero. This is because division by zero is undefined in mathematics. In other words, there is no number that you can divide by zero and get a meaningful, finite result. That’s why we must always ensure that the denominator of a fraction does not become zero for any value of the variable involved.
In this particular problem, the denominator is given as 3x + 5. To find the value that makes the expression undefined, we must find when the denominator equals zero. That is, we need to solve the equation 3x + 5 = 0.
To isolate x, we begin by moving constants to the other side of the equation. Subtracting 5 from both sides gives us 3x = -5. Next, we divide both sides by 3 to isolate x, resulting in x = -5/3. This value of x is critical because if we plug it back into the original expression, the denominator becomes zero, which is not allowed in mathematics.
Therefore, we conclude that the expression is undefined at x = -5/3, and that is the value that must be excluded from the domain of any function or expression that contains 3x + 5 in the denominator. Identifying these values is crucial when simplifying, solving, or graphing rational expressions, as they indicate vertical asymptotes or points of discontinuity.
