Math Problem Statement
Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. 2 x plus 4 less than 10
Solution
Let's solve the inequality .
Step-by-Step Solution:
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Subtract 4 from both sides to isolate the term with :
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Divide both sides by 2 to solve for :
Interval Notation:
The solution set for is all values less than 3, which can be expressed in interval notation as:
Graph on a Number Line:
On a number line, this would be an open interval to the left of 3, meaning we don't include 3 (since the inequality is strict).
- Draw a number line.
- Place an open circle at to indicate that 3 is not included.
- Shade everything to the left of 3 to represent all values less than 3.
Would you like me to graph this for you?
Related Questions:
- How do you solve inequalities that involve multiplication or division by negative numbers?
- What changes in the interval notation if the inequality was ?
- How do you solve compound inequalities, such as and ?
- How would the solution change if the inequality was ?
- What is the difference between strict and non-strict inequalities in interval notation?
Tip: Always remember, when dividing or multiplying by a negative number in an inequality, the inequality sign flips!
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Interval Notation
Formulas
Linear Inequality: ax + b < c
Interval Notation
Theorems
Properties of Inequalities
Number Line Representation
Suitable Grade Level
Grades 6-8