Lang Undergraduate Algebra Solutions Upd Official

Use the UPD solutions to verify your own work, not to copy. Lang’s problems often have multiple correct paths. If your answer differs from the solution set, it might be a sign of a new insight—or a hidden mistake. Check your reasoning.

Attempt every problem for 45 minutes without looking at the solutions. If you cannot make progress after 45 minutes, you have permission to look. But only look at the first line of the solution.

Problem: Solve the equation $$2x + 5 = 11$$ for $$x$$. lang undergraduate algebra solutions upd

Solution:

To solve for $$x$$, we need to isolate $$x$$ on one side of the equation. Use the UPD solutions to verify your own work, not to copy

$$2x + 5 = 11$$

Subtract 5 from both sides:

$$2x = 11 - 5$$

$$2x = 6$$

Divide both sides by 2:

$$x = 3$$