Answered

Solve |x + 7| < 6


A)

–13 < x < –1

B)

–1 < x < –13

C)

–13 < x and x > –1

D)

–13 < x or x < –1

Answer :

Answer:

A) - 13 < x < - 1

Step-by-step explanation:

1) Rewrite the inequality without the absolute value.

[tex] - 6 < x + 7 < 6[/tex]

2) Subtract 7 from the whole equation.

[tex] - 6 - 7 < x < 6 - 7[/tex]

3) Simplify.

[tex] - 13 < x < - 1[/tex]

Therefor, the answer is the first option.

Answer:

A) –13 < x < –1

Step-by-step explanation:

|x + 7| < 6

Separate into possible cases

[tex]x + 7 < 6 \\x +7 \geq 0[/tex]

Solve the inequalities

[tex]x < - 1, x \geq -7\\x > -13, x < -7[/tex]

Find the intersections

[tex]x = (-7, -1)\\x = (-13, -7)[/tex]

Find the union

Answer: A) –13 < x < –1

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