6 x __ = 9
6 times what number equals 9
The Correct Answer and Explanation is:
To solve the equation ( 6 \times _ = 9 ), we need to determine what number, when multiplied by 6, equals 9. This can be solved using division.
Step 1: Set up the equation
The equation is:
[
6 \times x = 9
]
where ( x ) represents the unknown number we need to find.
Step 2: Solve for ( x )
To isolate ( x ) on one side of the equation, we need to perform the opposite operation of multiplication, which is division. Divide both sides of the equation by 6:
[
x = \frac{9}{6}
]
Step 3: Simplify the fraction
The fraction ( \frac{9}{6} ) can be simplified. Both 9 and 6 have a common factor of 3. To simplify the fraction, divide both the numerator and the denominator by 3:
[
x = \frac{9 \div 3}{6 \div 3} = \frac{3}{2}
]
Thus, the solution to the equation is:
[
x = \frac{3}{2} \quad \text{or} \quad x = 1.5
]
Step 4: Verify the solution
To check our work, substitute ( x = 1.5 ) back into the original equation:
[
6 \times 1.5 = 9
]
Since the equation is correct, ( x = 1.5 ) is indeed the solution.
Explanation of the Process
To solve for ( x ), we used basic algebraic principles. The equation ( 6 \times x = 9 ) is a simple multiplication equation, and isolating the variable involves dividing both sides of the equation by 6 to undo the multiplication. Simplifying the resulting fraction gave us the final answer. In everyday language, this process is like asking, “What number, when multiplied by 6, will give 9?” Dividing 9 by 6 gives the answer directly, which in this case is ( 1.5 ).