Math Problem Statement
Solve
|
2
x
+
3
|
+
4
<
5
and write the solution in interval notation.
(If there is no solution, enter your answer as
∅
.)
Provide your answer below:
Solution
To solve the inequality:
Step 1: Subtract 4 from both sides of the inequality:
Step 2: Now, solve the absolute value inequality. This implies that:
Step 3: Solve for by subtracting 3 from all parts of the inequality:
Step 4: Divide the entire inequality by 2:
Thus, the solution in interval notation is:
Would you like further details or have any questions? Here are 5 related questions:
- What does the absolute value represent in an inequality?
- How would you solve an absolute value inequality with a greater-than symbol?
- What happens when you have multiple absolute value terms in an inequality?
- How would you graph the solution of an absolute value inequality?
- How do you handle absolute values in equations versus inequalities?
Tip: Remember that for absolute value inequalities, you always break them down into two cases—one for the positive and one for the negative scenario.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Absolute Value Inequalities
Formulas
|A| < B
Solving linear inequalities
Theorems
Absolute value inequality theorem
Suitable Grade Level
Grades 8-10