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How do you solve #|x + 13| = 2x + 1#?

Answer 1

Eli Assouline

Socratic graph is pointer to the solution x = 12/

chart{|x+13|-2x-1 [11.5, 12.5, -.5,.5]}

The answer is shown as x = 12 on the function's graph.

From an algebraic perspective,

When #x >=-13, x+13 = 2x + 1#,

giving a valid solution.#x = 12 > -13#.

When #x <=-13, -(x+13) = 2x + 1#,

giving invalid solution.#x =-(1 4)/3 > -13#.

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Answer 2

Savannah Anderson

To solve the equation |x + 13| = 2x + 1, you need to consider two cases: when the expression inside the absolute value is positive and when it is negative. When x + 13 is positive, the equation becomes x + 13 = 2x + 1. When x + 13 is negative, the equation becomes -(x + 13) = 2x + 1. Solve each case separately to find the possible values of x.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.