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Choose the correct words to fill in the blanks below. boundary solution set broken linear inequality solid 1. A in two variables is any expression that can be put in the form \( a x+b x<0 \), where the inequality symbol can be \( <,>, \leq \), or \( \geq \). 2. The \( \square \) 3. The \( \square \) for a linear inequality is a section of the coordinate plane. the inequality symbol with an equals sign and graphing the resulting equation. 4. Use a \( \square \) line for the boundary of a linear inequality if the original inequality symbol was \( \geq \) or \( \leq \). 5. Use a \( \square \) symbol was \( > \) or \( < \).

Ask by West Reese. in the United States
Mar 20,2025

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Answer

1. A **linear inequality** in two variables is any expression that can be put in the form \( ax + b < 0 \), where the inequality symbol can be \( <, >, \leq \), or \( \geq \). 2. The **solution set**. 3. The **boundary** for a linear inequality is a section of the coordinate plane. 4. Use a **solid** line for the boundary of a linear inequality if the original inequality symbol was \( \geq \) or \( \leq \). 5. Use a **broken** line for the boundary of a linear inequality if the original inequality symbol was \( > \) or \( < \).

Solution

Let's fill in the blanks with the appropriate words based on the context of linear inequalities: 1. A **linear inequality** in two variables is any expression that can be put in the form \( ax + b < 0 \), where the inequality symbol can be \( <, >, \leq \), or \( \geq \). 2. The **solution set**. 3. The **boundary** for a linear inequality is a section of the coordinate plane. 4. Use a **solid** line for the boundary of a linear inequality if the original inequality symbol was \( \geq \) or \( \leq \). 5. Use a **broken** line for the boundary of a linear inequality if the original inequality symbol was \( > \) or \( < \). So the completed sentences are: 1. A **linear inequality** in two variables is any expression that can be put in the form \( ax + b < 0 \), where the inequality symbol can be \( <, >, \leq \), or \( \geq \). 2. The **solution set**. 3. The **boundary** for a linear inequality is a section of the coordinate plane. 4. Use a **solid** line for the boundary of a linear inequality if the original inequality symbol was \( \geq \) or \( \leq \). 5. Use a **broken** line for the boundary of a linear inequality if the original inequality symbol was \( > \) or \( < \).

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The Deep Dive

A linear inequality in two variables is any expression that can be put in the form \( ax + b < 0 \), where the inequality symbol can be \( <, >, \leq \), or \( \geq \). The boundary solution set is the graph of the related linear equation obtained by replacing the inequality symbol with an equals sign and graphing the resulting equation. Use a solid line for the boundary of a linear inequality if the original inequality symbol was \( \geq \) or \( \leq \). Use a broken line for the boundary if the inequality symbol was \( > \) or \( < \).

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