Find the root of the equation 5(x + 8) = 9.

Step-by-step solution

1. 1

   Notice the bracket is multiplied by a single number. When the entire left side is one product, undoing the multiplication is cheaper than distributing. Dividing both sides by $5$ keeps the equation balanced:

   $x+8=\frac{9}{5}.$

2. 2

   Isolate x by subtracting 8. Write $8$ over the same denominator so the subtraction is exact rather than decimal:

   $x=\frac{9}{5}-8=\frac{9}{5}-\frac{40}{5}=-\frac{31}{5}.$

3. 3

   Convert to a decimal if the answer box expects one.

   $x=-\frac{31}{5}=-6.2.$

4. 4

   Compare with the expand-first route. Distributing gives $5x+40=9$, then $5x=-31$, then $x=-31/5$ — the same answer in three steps instead of two. Both are correct; the division-first route simply avoids creating and then removing the $40$.

5. 5

   Substitute back to check.

   $5(-6.2+8)=5(1.8)=9,$

   which matches the right-hand side, so $x=-6.2$ is the root.