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 2x+4<102x + 4 < 10.

Step-by-Step Solution:

  1. Subtract 4 from both sides to isolate the term with xx: 2x+44<1042x + 4 - 4 < 10 - 4 2x<62x < 6

  2. Divide both sides by 2 to solve for xx: 2x2<62\frac{2x}{2} < \frac{6}{2} x<3x < 3

Interval Notation:

The solution set for xx is all values less than 3, which can be expressed in interval notation as: (,3)(-\infty, 3)

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 x=3x = 3 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:

  1. How do you solve inequalities that involve multiplication or division by negative numbers?
  2. What changes in the interval notation if the inequality was 2x+4102x + 4 \leq 10?
  3. How do you solve compound inequalities, such as 2x+4<102x + 4 < 10 and x>1x > 1?
  4. How would the solution change if the inequality was 2x+4>102x + 4 > 10?
  5. 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