solve.

\8 - |x + 3| = 1\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution(s) is/are $ \quad $.
(simplify your answer. type an integer or a fraction. use a comma to separate answers as needed.)

b. there is no solution.

Question

solve.

\8 - |x + 3| = 1\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution(s) is/are $ \quad $.
(simplify your answer. type an integer or a fraction. use a comma to separate answers as needed.)

b. there is no solution.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Equations" ], "new_concepts": [], "current_concepts": [ "Absolute Value Equations" ] } ## Isolate the absolute value expression $$ \begin{aligned} 8 - |x + 3| &= 1 \ -|x + 3| &= 1 - 8 \ -|x + 3| &= -7 \ |x + 3| &= 7 \end{aligned} $$ ## Set up and solve the two cases $$ \begin{aligned} x + 3 = 7 \quad &\text{or} \quad x + 3 = -7 \ x = 4 \quad &\text{or} \quad x = -10 \end{aligned} $$ ## Verify the solutions $$ \begin{aligned} 8 - |4 + 3| &= 8 - 7 = 1 \ 8 - |-10 + 3| &= 8 - |-7| = 8 - 7 = 1 \end{aligned} $$

(A) The solution(s) is/are 4, -10

(B) There is no solution.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Isolate the absolute value expression

Set up and solve the two cases

Verify the solutions

Answer: