Solve for x: 32.63x + 4.545 = 10.

Step-by-step solution

1. 1

   Plan the two operations in the right order. The variable is first multiplied by $32.63$ and then has $4.545$ added. Undoing works in reverse: subtract the constant, then divide by the coefficient. Dividing first would force distributing the division over both terms and invites mistakes.

2. 2

   Subtract 4.545 from both sides.

   $32.63x=10-4.545=5.455$

   Aligning the decimal points matters here: $10.000-4.545=5.455$.

3. 3

   Estimate the answer before dividing. $5.455$ is roughly one sixth of $32.63$, so expect $x\approx0.17$. Any result near $1$ or near $0.02$ would signal a misplaced decimal.

4. 4

   Divide both sides by 32.63.

   $x=\frac{5.455}{32.63}=\frac{5455}{32630}=\frac{1091}{6526}$

   Multiplying top and bottom by $1000$ clears the decimals, and dividing by the common factor $5$ gives the reduced exact fraction.

5. 5

   Convert to a decimal.

   $x=0.1671774\ldots\approx0.1672$

   This matches the estimate of about $0.17$ ✓.

6. 6

   Verify by substitution. $32.63\times0.16717744+4.545=5.455000+4.545=10.000000$ ✓.