Question

Write the inequality in the form of a<x<b. |x| < c^2

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To write the inequality |x| < c^2 in the form of a < x < b, we need to consider two separate cases:

Case 1: x is positive

In this case, the inequality |x| < c^2 becomes x < c^2.

Case 2: x is negative

In this case, the inequality |x| < c^2 becomes -x < c^2. To solve for x, we need to multiply both sides of the inequality by -1, but since we are multiplying by -1, we need to change the direction of the inequality, giving us -x > -c^2. Finally, multiplying both sides by -1 gives us x > -c^2.

Combining both cases, we can write the inequality in the form of a < x < b as -c^2 < x < c^2.

Therefore, the inequality |x| < c^2 can be written as -c^2 < x < c^2.

Answer: -c^2 < x < c^2

Case 1: x is positive

In this case, the inequality |x| < c^2 becomes x < c^2.

Case 2: x is negative

In this case, the inequality |x| < c^2 becomes -x < c^2. To solve for x, we need to multiply both sides of the inequality by -1, but since we are multiplying by -1, we need to change the direction of the inequality, giving us -x > -c^2. Finally, multiplying both sides by -1 gives us x > -c^2.

Combining both cases, we can write the inequality in the form of a < x < b as -c^2 < x < c^2.

Therefore, the inequality |x| < c^2 can be written as -c^2 < x < c^2.

Answer: -c^2 < x < c^2

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