Questions: Solve the following inequality. Write the inequality in interval notation, and graph it. 6 r+1=2 r-23 To solve the given inequality, first use the addition property of inequality to get all terms with variables on one side of the inequality and all numbers on the other side. What term should be subtracted from each side of the inequality to isolate the variable term on the left side? Subtract 2 r from each side of the inequality. 6 x+1 geq 2 r-23 6 i+1-2 r geq 2 r-23-2 r 4 r geq-23

Solve the following inequality. Write the inequality in interval notation, and graph it. 6 r+1=2 r-23 To solve the given inequality, first use the addition property of inequality to get all terms with variables on one side of the inequality and all numbers on the other side. What term should be subtracted from each side of the inequality to isolate the variable term on the left side? Subtract 2 r from each side of the inequality. 6 x+1 geq 2 r-23 6 i+1-2 r geq 2 r-23-2 r 4 r geq-23
Transcript text: Solve the following inequality. Write the inequality in interval notation, and graph it. \[ 6 r+1=2 r-23 \] To solve the given inequality, first use the addition property of inequality to get all terms with variables on one side of the inequality and all numbers on the other side. What term should be subtracted from each side of the inequality to isolate the variable term on the left side? Subtract 2 r from each side of the inequality. \[ \begin{aligned} 6 x+1 & \geq 2 r-23 \\ 6 i+1-2 r & \geq 2 r-23-2 r \\ 4 r & \geq-23 \end{aligned} \]
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Solution

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Solution Steps

To solve the given equation, first, isolate the variable \( r \) by moving all terms involving \( r \) to one side and constant terms to the other side. Then, solve for \( r \) by performing basic arithmetic operations. Finally, express the solution in interval notation and graph it.

To solve the given inequality, we need to follow the steps outlined in the problem. Let's go through the solution step by step.

Step 1: Set Up the Inequality

The given equation is: \[ 6r + 1 = 2r - 23 \]

Step 2: Move Variable Terms to One Side

Subtract \(2r\) from both sides to get all terms with the variable on one side: \[ 6r + 1 - 2r = 2r - 23 - 2r \] Simplifying, we have: \[ 4r + 1 = -23 \]

Step 3: Isolate the Variable

Subtract 1 from both sides to isolate the term with the variable: \[ 4r + 1 - 1 = -23 - 1 \] Simplifying, we have: \[ 4r = -24 \]

Step 4: Solve for the Variable

Divide both sides by 4 to solve for \(r\): \[ r = \frac{-24}{4} \] Simplifying, we have: \[ r = -6 \]

Final Answer

The solution to the equation is: \[ \boxed{r = -6} \]

Since the original problem was an equation rather than an inequality, there is no interval notation or graph required. The solution is simply \(r = -6\).

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