# Writing Equations

## Algebra: Writing Equations

Read the following SAT test question and then select the correct answer.

Approach all math questions the same way.  Read the question carefully to avoid making careless mistakes.  Identify the bottom line, the question you must solve, and note it on your test.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to verify that the answer addresses the bottom line.

First, 3 is subtracted from x and the square root of the difference is taken. Then, 5 is added to the result, giving a final result of 9. What is the value of x?

Bottom line: x = ?

Assess your options: You could try to plug in answer choices and see which one equals 9, but you may have to write and solve the equation multiple times.  Instead, translate the two sentences into “math” and use algebra to find x.

Attack the problem: Work through the words step by step.  First, 3 is subtracted from x.  Write:

x – 3

The square root of the difference is taken.  That means both numbers involved in the difference are under the radical.

$\sqrt{x-3}$

Then 5 is added and the final result is 9.

$\sqrt{x-3}\, +5=9$

Now that you have your equation written, all you have to do is solve for x:

$\sqrt{x-3}\, +5=9$           (subtract 5 from each side)
$\sqrt{x-3}\, =4$                 (square each side to remove the radical)
$x - 3= 16$
$x = 19$

Loop Back: You solved for your bottom line, so look down at the answer choices.

(A) 3
(B) 4
(C) 5
(D) 16
(E) 19