If 4x + y = 7 is a true equation, what would be the value of -5(4x + y)?
Understand the Problem
The question asks to find the value of the expression -5(4x + y) given that the equation 4x + y = 7 is true. We need to substitute the value from the equation into the expression.
Answer
The value of $-5(4x + y)$ is $-35$.
Answer for screen readers
The value of $-5(4x + y)$ is $-35$.
Steps to Solve
- Substitute the known expression
We know from the problem that $4x + y = 7$. We will substitute this value into the expression $-5(4x + y)$.
- Write the expression in terms of 7
Now, replace $4x + y$ in the expression with 7:
$$ -5(4x + y) = -5(7) $$
- Calculate the final value
Now we will calculate $-5 \times 7$:
$$ -5 \times 7 = -35 $$
The value of $-5(4x + y)$ is $-35$.
More Information
The expression $-5(4x + y)$ is a linear transformation of the input $4x + y$. Substituting a known value into the expression simplifies evaluation and leads to quick computation.
Tips
- Not substituting correctly: Failing to replace $4x + y$ with 7 would lead to an incorrect answer. Always ensure you're using the correct equation.
- Sign errors: Be cautious with multiplying negative numbers, as it's a common mistake to miscalculate the sign in the final answer.
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