Math Problem Statement

Solve the inequality and graph the solution on the line provided: 2 + 2x < -12

Solution

Let's solve the inequality and then graph the solution.

Inequality:

2+2x<122 + 2x < -12

Step 1: Subtract 2 from both sides

2x<1222x < -12 - 2 2x<142x < -14

Step 2: Divide by 2 to isolate xx

x<142x < \frac{-14}{2} x<7x < -7

Inequality Notation:

x<7x < -7

Graphing:

On the number line, you'd plot an open circle at x=7x = -7 to indicate that 7-7 is not included in the solution. Then shade everything to the left of 7-7 because the inequality is x<7x < -7.

Would you like more details or further clarification?

Here are some related questions:

  1. How would the solution change if the inequality were 2+2x122 + 2x \leq -12?
  2. Can you explain why dividing by a positive number doesn't flip the inequality?
  3. How do you graph a solution for x7x \geq -7?
  4. What is the solution to the inequality 2+2x>122 + 2x > -12?
  5. How do you solve an inequality if you have a fraction, like 2x<3\frac{2}{x} < 3?

Tip: Always remember that dividing or multiplying by a negative number flips the inequality sign!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Equations

Formulas

Basic algebraic manipulation
Solving linear inequalities

Theorems

Properties of inequalities: When dividing by a positive number, the inequality sign remains the same

Suitable Grade Level

Grades 7-9