If we multiply a number by 5/2 and add 2/3 to the product, we get -7/12. Find the number.
-1/2
Explanation
The question requires setting up a linear equation based on the given word problem. Let the unknown number be x. Following the operations described, multiplying x by 5/2 gives (5/2)x, and adding 2/3 gives (5/2)x + 2/3. This expression is set equal to -7/12. Solving this linear equation involves transposing the constant term to the Right Hand Side (RHS), finding a common denominator to perform the subtraction, and then multiplying by the reciprocal of the coefficient of x to find the value of the unknown number.
Solution Steps
Step 1: Let the required number be x. Form the equation based on the given statement: (5/2)x + 2/3 = -7/12
Step 2: Transpose 2/3 to the RHS: (5/2)x = -7/12 - 2/3
Step 3: Find a common denominator for the RHS (which is 12) and subtract: (5/2)x = -7/12 - 8/12 = -15/12
Step 4: Simplify the RHS: (5/2)x = -5/4
Step 5: Multiply both sides by the reciprocal of 5/2, which is 2/5: x = (-5/4) × (2/5) = -1/2