Questions: For each value of x, determine whether it is a solution to 36 > 25 + x. x Is it a solution? Yes No --------- 9 6 14 11

For each value of x, determine whether it is a solution to 36 > 25 + x. x Is it a solution? Yes No --------- 9 6 14 11
Transcript text: For each value of $x$, determine whether it is a solution to $36>25+x$. \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{$x$} & \multicolumn{2}{|c|}{ Is it a solution? } \\ \cline { 2 - 3 } & Yes & No \\ \hline 9 & $\bigcirc$ & $\bigcirc$ \\ \hline 6 & $\bigcirc$ & $\bigcirc$ \\ \hline 14 & $\bigcirc$ & $\bigcirc$ \\ \hline 11 & $\bigcirc$ & $\bigcirc$ \\ \hline \end{tabular}
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Solution

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Solution Steps

To determine whether each value of \( x \) is a solution to the inequality \( 36 > 25 + x \), we need to check if substituting each value of \( x \) into the inequality results in a true statement. If the inequality holds true, then the value is a solution; otherwise, it is not.

Step 1: Set Up the Inequality

We are given the inequality \( 36 > 25 + x \). We need to determine if each value of \( x \) satisfies this inequality.

Step 2: Substitute Each Value of \( x \)

Substitute each given value of \( x \) into the inequality and check if the inequality holds true.

  1. For \( x = 9 \): \[ 36 > 25 + 9 \implies 36 > 34 \] This is true.

  2. For \( x = 6 \): \[ 36 > 25 + 6 \implies 36 > 31 \] This is true.

  3. For \( x = 14 \): \[ 36 > 25 + 14 \implies 36 > 39 \] This is false.

  4. For \( x = 11 \): \[ 36 > 25 + 11 \implies 36 > 36 \] This is false.

Final Answer

  • For \( x = 9 \), the inequality is true: \(\boxed{\text{Yes}}\)
  • For \( x = 6 \), the inequality is true: \(\boxed{\text{Yes}}\)
  • For \( x = 14 \), the inequality is false: \(\boxed{\text{No}}\)
  • For \( x = 11 \), the inequality is false: \(\boxed{\text{No}}\)
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