If x is an integer, how many values of x will satisfy the equation ||x + 3| + 2| = 4?

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Official Explanation

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The key point to remember is that the absolute value of any expression is always non-negative. Therefore, |x + 3| must be greater than or equal to 0. To simplify the equation, let's set |x + 3| = y. This transforms our equation into |y + 2| = 4. We need to solve this equation in two parts: first, as if the…

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What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.