Math Problem Statement
Solution
The inequality provided is:
Let's solve this step-by-step to find the equivalent inequality.
Step 1: Expand both sides.
- Left side:
- Right side:
Thus, the inequality becomes:
Step 2: Combine like terms.
-
Add to both sides:
-
Add to both sides:
Step 3: Solve for .
- Divide both sides by :
Thus, the inequality is , but we are looking for an inequality that matches the format in the options.
Step 4: Compare to the options provided.
We need to match the inequality with one of the options. From the options, we see they are looking at the equivalent form in terms of .
The inequality becomes:
So, the correct answer is Option D: .
Would you like further details or have any other questions?
Here are 5 related questions to expand on this topic:
- How do you solve inequalities with negative coefficients?
- What is the effect of multiplying or dividing an inequality by a negative number?
- How do you graph the solution of an inequality on a number line?
- Can you provide a real-world example where inequalities are used?
- What are the key differences between solving an inequality and solving an equation?
Tip: When solving inequalities, remember to flip the inequality sign when multiplying or dividing by a negative number.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Linear Equations
Formulas
Distributive Property
Combining Like Terms
Theorems
Properties of Inequalities
Suitable Grade Level
Grades 8-10