Math linear inequalities
Understand the Problem
The question is asking about linear inequalities, which are mathematical statements that express the relationship between two expressions using inequality signs. This involves understanding how to solve inequalities and graph them on a number line.
Answer
The solution to the inequality is $x < 2$.
Answer for screen readers
The solution to the inequality is $x < 2$.
Steps to Solve
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Identify the inequality Start by understanding the linear inequality you need to solve. For example, let's say we have the inequality $2x + 3 < 7$.
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Isolate the variable To solve for $x$, we need to isolate it on one side of the inequality:
Subtract $3$ from both sides: $$ 2x < 7 - 3 $$ This simplifies to $2x < 4$.
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Solve for the variable Now, divide both sides by $2$ to solve for $x$: $$ x < \frac{4}{2} $$ This simplifies to $x < 2$.
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Graph the solution on a number line Once you have $x < 2$, you can represent this on a number line. Place an open circle at $2$ (indicating that $2$ is not included) and shade the line to the left to show that all values less than $2$ are included in the solution.
The solution to the inequality is $x < 2$.
More Information
Linear inequalities represent a range of solutions rather than a single value, and graphing them can help visualize those solutions. The open circle indicates that the endpoint is not included in the solution set.
Tips
- Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
- Misplacing the parenthesis or not using the correct sign when graphing the solution on a number line.
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