Is the equation 7−4⋅7349√=7 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)

1 answer

To determine if the equation \( 7 - 4 \cdot 7349 \sqrt{} = 7 \) is true or false, we need to simplify the left-hand side of the equation.

The left-hand side is \( 7 - 4 \cdot 7349\sqrt{} \).

First, note that the square root symbol \( \sqrt{} \) requires a number to evaluate. If we assume it means the square root of some number \( x \) (i.e., \( \sqrt{x} \)), we can rewrite it as:

\[ 7 - 4 \cdot 7349 \sqrt{x} \]

Now we need to assess if this equals \( 7 \):

  1. Isolate the equation: \[ 7 - 4 \cdot 7349 \sqrt{x} = 7 \]

  2. Subtract 7 from both sides: \[ -4 \cdot 7349 \sqrt{x} = 0 \]

  3. Since multiplying by -4 affects the equality, we divide both sides by -4: \[ 7349 \sqrt{x} = 0 \]

For this equation to hold true, it must be that: \[ \sqrt{x} = 0 \]

Which implies: \[ x = 0 \]

Thus, if \( x = 0 \), then the left-hand side simplifies to: \[ 7 - 4 \cdot 7349 \cdot 0 = 7 \]

Therefore, the original equation holds true if \( \sqrt{} \) is interpreted as \(\sqrt{0}\). However, if no value for \( x \) is specified, we cannot evaluate it as a true statement generally without making assumptions.

Based on common interpretations, unless explicitly stated, the assertion \( 7 - 4 \cdot 7349 \sqrt{} = 7 \) is generally considered False because we cannot interpret \( \sqrt{} \) without knowing its argument.

Final Answer: False. The equation cannot be verified without a specific value under the square root.