Solve the equation 5x + 7 = 2. Give an exact solution.

Step-by-step solution

1. 1

   Decide the order of operations to undo. The left side builds $x$ by multiplying by $5$ and then adding $7$. To isolate $x$ you undo those steps in reverse: subtract first, divide second. Dividing first would force you to divide $7$ by $5$ as well, creating an unnecessary fraction.

2. 2

   Subtract 7 from both sides.

   $5x+7-7=2-7\ \Longrightarrow\ 5x=-5$

   The right side is negative, which already tells you $x$ will be negative since $5>0$.

3. 3

   Divide both sides by 5.

   $x=\frac{-5}{5}=-1$

   This is exact — no rounding is involved, because $-5$ is a whole multiple of $5$.

4. 4

   Substitute back to check.

   $5(-1)+7=-5+7=2\ \checkmark$

   The left side reproduces the right side exactly, so $x=-1$ is the unique solution. The equation is linear with a nonzero coefficient on $x$, so there is exactly one solution — no extra roots to look for.