For the given expression, identify the terms, like terms, coefficients, and constant terms. Then simplify the expression:

Question

For the given expression, identify the terms, like terms, coefficients, and constant terms. Then simplify the expression:
-1 + 4x + 6x - 20

GPT-4o mini · Answer

To analyze the expression $-1 + 4x + 6x - 20$, we can identify the different components: 1. **Terms:** The expression consists of the following terms: - $-1$ (constant term) - $4x$ (variable term) - $6x$ (variable term) - $-20$ (constant term) 2. **Like terms:** Like terms are terms that have the same variable raised to the same power. In this case, the like terms are: - $4x$ and $6x$ (both terms containing the variable $x$) - $-1$ and $-20$ (constant terms) 3. **Coefficients:** The coefficients are the numerical factors in front of the variable terms: - The coefficient of $4x$ is $4$. - The coefficient of $6x$ is $6$. - The constant terms $-1$ and $-20$ do not have coefficients associated with any variable. 4. **Constant terms:** The constant terms in the expression are $-1$ and $-20$. Now, to **simplify** the expression, we will combine like terms. The variable terms $4x$ and $6x$ can be combined: $$ 4x + 6x = 10x $$ The constant terms $-1$ and $-20$ can also be combined: $$ -1 - 20 = -21 $$ Putting it all together, the simplified expression is: $$ 10x - 21 $$ Thus, the final simplified form of the expression $-1 + 4x + 6x - 20$ is: $$ \boxed{10x - 21} $$