Find the approximate value of x from the given expression: 29.38 × 37.05 ÷ x +…

Concept:

To find an unknown x in an equation of the form (a × b) ÷ x + c = d, first isolate the term containing x by moving the constant c to the other side, then invert the division to convert it into a simple multiplication for x. Approximate the final quotient only at the very last step, after all algebraic rearrangement is complete.

Application:

1. Write the given equation: 29.38 × 37.05 ÷ x + 7.45 = 100.5

2. Subtract 7.45 from both sides to isolate the term with x: 29.38 × 37.05 ÷ x = 100.5 − 7.45 = 93.05

3. Multiply both sides by x and divide by 93.05 to isolate x: x = (29.38 × 37.05) ÷ 93.05

4. Compute the numerator: 29.38 × 37.05 = 1088.529

5. Divide: x = 1088.529 ÷ 93.05 ≈ 11.698

6. Round the quotient to the nearest whole number, as the question asks for an approximate value: x ≈ 12

Cross-check:

Substituting the unrounded value x = 11.698 back into the original expression gives 1088.529 ÷ 11.698 + 7.45 = 93.05 + 7.45 = 100.5, which matches the right-hand side exactly — confirming the rearrangement is correct before rounding.

Hence, the approximate value of x is 12.