Solve for x: 32.63x + 4.545 = 15.

Step-by-step solution

1. 1

   Undo the operations in reverse order. The constant $4.545$ was added last, so remove it first; only then divide by the coefficient $32.63$.

2. 2

   Subtract 4.545 from both sides.

   $32.63x=15-4.545=10.455$

3. 3

   Estimate before dividing. $10.455$ is a bit under a third of $32.63$, so expect $x$ slightly under $0.32$.

4. 4

   Divide by 32.63 and clear the decimals.

   $x=\frac{10.455}{32.63}=\frac{10455}{32630}=\frac{2091}{6526}$

   (Both were multiplied by $1000$, then reduced by the common factor $5$.)

5. 5

   Evaluate and round carefully.

   $x=0.32041066\ldots$

   To four decimal places this is $0.3204$, since the next digit is $1$. A rounding of $0.3203$ is sometimes given for this equation, but it truncates rather than rounds — the exact value $0.320410\ldots$ is nearer to $0.3204$.

6. 6

   Verify by substitution. $32.63\times0.32041066+4.545=10.455000+4.545=15.000000$ ✓, matching the pre-division estimate of just under $0.32$ ✓.