Question
Solve the inequality. Graph the solutions.
minus33plusStartAbsoluteValue 4 x minus 10 EndAbsoluteValueless than or equalsminus7
Question content area bottom
Part 1
Select the correct choice below and fill in any answer boxes in your choice.
A.
The solution is
enter your response hereless than or equalsxless than or equals
enter your response here. (Type integers or simplified fractions.)
B.
The solution is xless than or equals
enter your response here or xgreater than or equals
enter your response here. (Type integers or simplified fractions.)
C.
The solution is xequals
enter your response here. (Type an integer or a simplified fraction.)
D.
The solution is all real numbers.
E.
There is no solution.
minus33plusStartAbsoluteValue 4 x minus 10 EndAbsoluteValueless than or equalsminus7
Question content area bottom
Part 1
Select the correct choice below and fill in any answer boxes in your choice.
A.
The solution is
enter your response hereless than or equalsxless than or equals
enter your response here. (Type integers or simplified fractions.)
B.
The solution is xless than or equals
enter your response here or xgreater than or equals
enter your response here. (Type integers or simplified fractions.)
C.
The solution is xequals
enter your response here. (Type an integer or a simplified fraction.)
D.
The solution is all real numbers.
E.
There is no solution.
Answers
GPT-5 mini
Interpret the inequality as: -33 + |4x - 10| ≤ -7.
Add 33 to both sides: |4x - 10| ≤ 26.
Solve the compound inequality: -26 ≤ 4x - 10 ≤ 26
→ -16 ≤ 4x ≤ 36
→ -4 ≤ x ≤ 9.
So choose A with -4 ≤ x ≤ 9. Graph: closed dot at -4, closed dot at 9, solid segment joining them.
Add 33 to both sides: |4x - 10| ≤ 26.
Solve the compound inequality: -26 ≤ 4x - 10 ≤ 26
→ -16 ≤ 4x ≤ 36
→ -4 ≤ x ≤ 9.
So choose A with -4 ≤ x ≤ 9. Graph: closed dot at -4, closed dot at 9, solid segment joining them.