Final answer:
The question involves finding the value of a variable q that will result in an expression greater than 6, using algebraic methods for solving inequalities and operations with fractions.
Step-by-step explanation:
The question is asking to solve for a value of a variable q that, when plugged into a certain expression, will result in a value greater than 6. To approach this, we must understand that q can have many different values, and we use algebra to determine the specific value based on the given expression. For example, if we have the equation q = 2/3 of x, and we want this to be greater than 6, we can set up an inequality: 2/3 x > 6. By algebraically solving for x, we find that x must be greater than 9 for this inequality to be true.
Understanding how operations on fractions work is key to solving such problems. If we add fractions, like 1/2 + 1/3, it's intuitive to find a common denominator, which in this case would be 6, hence the sum becomes 3/6 + 2/6, which equals 5/6. Algebraic manipulation often involves ensuring that both sides of an equation or inequality maintain balance while we perform operations to isolate variables. This is fundamental when working with variables and expressions.