Problem 39 - Algebra 1

Question

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$5+s>8 ; 4$$

Step-by-Step Solution

Answer

Yes, 4 is a solution for the given inequality because \(9 > 8\) is a true statement.

Step 1 : Analysing the inequality

The given inequality is \(5 + s > 8\). The task requires to check whether 4 is a solution of this inequality.

Step 2 : Substitution

Substitute the value of \(s = 4\) into the inequality. It becomes \(5 + 4 > 8\).

Step 3 : Calculation

After substituting the value of \(s\), calculate the left side of inequality. It will be \(9 > 8\).

Key Concepts

Checking Solutions

When tasked with checking whether a number is a solution to an inequality, the goal is simply to see if it fits the condition of the inequality. In our context, the inequality is given as \(5 + s > 8\). We want to determine if the number 4 could replace \(s\) and still make the inequality true. To check this, you will substitute the given number into the inequality. Solving it afterward will either prove or disprove it as a solution. This process helps verify your understanding of inequalities and ensures accurate results, much like testing a hypothesis in science.

Substitution

Substitution is the process of replacing a variable with a given number to see if it satisfies an equation or inequality. Here, we substitute \(s = 4\) in the inequality \(5 + s > 8\). The result will give us a new inequality: \(5 + 4 > 8\).

• Write the original inequality.
• Replace \(s\) with 4 to get \(5 + 4 > 8\).

This step is crucial because it directly leads to understanding if the particular number makes the inequality true.

Calculation

After substitution, the next step is to perform any necessary calculations. This helps clarify whether the inequality holds true. In our example, substituting 4 for \(s\) gives us the expression \(5 + 4 > 8\).

• Calculate the left side: \(5 + 4 = 9\).
• Compare: \(9 > 8\).

This confirms that 9 is indeed greater than 8, showcasing that the inequality is satisfied when \(s = 4\). It shows how calculations play a pivotal role in solving mathematical problems.

Step-by-Step Solution

Breaking down a problem into distinct steps helps in unraveling complex problems, making them digestible and approachable. This approach aids in understanding the flow and logic involved in solving inequalities. Here's the breakdown: 1. **Analyzing the Inequality**: First, understand the inequality often involves looking at what needs to be proved or disproved. 2. **Substitution**: Replace the variable with the given number to test if it holds true. 3. **Calculation**: Perform necessary math to simplify and compare. This structured progression helps students grasp each phase separately, boosting confidence and clarity in handling similar exercises. It emphasizes the importance of organized thought processes in mathematics.