Answer
The provided statement does not make sense.
Work Step by Step
An equation is formed when two algebraic expressions are equated with equal sign. An equation uses variables to express the relationship between two or more attributes of something. Say relationship between temperature measured in Fahrenheit and measured in Celsius is represented by the equation;
\[F=32+\frac{9}{5}C\]
Solution set of this equation is values of temperature measured in Fahrenheit for the values measured in Celsius.
Given equation is\[7x+9=9\left( x+1 \right)-2x\].
Use distributive-property to solve this equation,
\[\begin{align}
& 7x+9=9x+9-2x \\
& 7x+9=9x-2x+9 \\
& 7x+9=7x+9 \\
\end{align}\]
See the equation \[7x+9=7x+9\]is true for every value of x.
For example, it is true for\[x=3\]. Just check it
\[\begin{align}
& 7x+9=7x+9 \\
& 7.3+9=7.3+9 \\
& 30=30
\end{align}\]
And this equation is also true for\[x=4\]. Again, check it
\[\begin{align}
& 7x+9=7x+9 \\
& 7.4+9=7.4+9 \\
& 37=37
\end{align}\]
Substitute any value of x makes the equation true in this case.
This means the given equation is true for any value of x and thus this equation has infinitely many solutions for x.
Therefore, the given statement that, “The number 3 satisfies the equation\[7x+9=9\left( x+1 \right)-2x\], so \[\left\{ 3 \right\}\]is the equation’s solution set” does not make any sense.
