Questions: If 7-x<5, then x>2.

Transcript text: If $7-x<5$, then $x>2$.

Solution

Solution Steps

To determine if the statement is true or false, we need to solve the inequality $7 - x < 5$ for $x$ and then check if the resulting inequality implies $x > 2$.

Step 1: Understand the Problem

We need to determine if the statement "If $7 - x < 5$, then $x > 2$" is true or false.

Step 2: Solve the Inequality $7 - x < 5$

First, we solve the inequality $7 - x < 5$.

\[ 7 - x < 5 \]

Subtract 7 from both sides:

x < 5 - 7 \]

Simplify the right-hand side:

x < -2 \]

Step 3: Solve for $x$

To solve for $x$, we need to divide both sides by -1. Remember that dividing by a negative number reverses the inequality sign.

\[ x > 2 \]

Step 4: Analyze the Statement

The statement "If $7 - x < 5$, then $x > 2$" is equivalent to saying that the solution to the inequality $7 - x < 5$ implies $x > 2$.

Since we have shown that solving $7 - x < 5$ results in $x > 2$, the statement is indeed true.

Final Answer

\[ \boxed{\text{True}} \]

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