Question Determine which values satisfy the inequality $\frac{2}{5} y - 13 > -15$ and mark them in the table.

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality $\frac{2}{5} y - 13 > -15$ .
2. We need to test the values $y = -10$ , $y = -5$ , and $y = 0$ to determine if they satisfy the inequality.
3. An $X$ will be placed in the appropriate column of the table to indicate whether each value is or is not a solution to the inequality.

STEP 2

First, we will solve the inequality for $y$ to find the range of values that satisfy it.
$\frac{2}{5} y - 13 > -15$

STEP 3

Add $13$ to both sides of the inequality to isolate the term with $y$ on one side.
$\frac{2}{5} y - 13 + 13 > -15 + 13$

STEP 4

Simplify both sides of the inequality.
$\frac{2}{5} y > -2$

STEP 5

Multiply both sides of the inequality by $\frac{5}{2}$ to solve for $y$ .
$y > -2 \times \frac{5}{2}$

STEP 6

Calculate the value on the right side of the inequality.
$y > -5$

STEP 7

Now we know that any value of $y$ greater than $-5$ is a solution to the inequality. We can now test each of the given values.

STEP 8

Test $y = -10$ by substituting it into the inequality.
$\frac{2}{5} (-10) - 13 > -15$

STEP 9

Calculate the left side of the inequality.
$\frac{2}{5} (-10) - 13 = -4 - 13$

STEP 10

Simplify the left side of the inequality.
$-4 - 13 = -17$

STEP 11

Compare the calculated value with $-15$ .
$-17 \not> -15$

STEP 12

Since $-17$ is not greater than $-15$ , $y = -10$ is not a solution to the inequality. Place an $X$ in the "Is Not a Solution" column for $y = -10$ .
\begin{tabular}{|r|r|r|} \cline { 2 - 3 } & Is a Solution & Is Not a Solution \\ \hline-10 & & X \\ \hline-5 & & \\ \hline 0 & & \\ \hline \end{tabular}

STEP 13

Test $y = -5$ by substituting it into the inequality.
$\frac{2}{5} (-5) - 13 > -15$

STEP 14

Calculate the left side of the inequality.
$\frac{2}{5} (-5) - 13 = -2 - 13$

STEP 15

Simplify the left side of the inequality.
$-2 - 13 = -15$

STEP 16

Compare the calculated value with $-15$ .
$-15 \not> -15$

STEP 17

Since $-15$ is not greater than $-15$ , $y = -5$ is not a solution to the inequality. Place an $X$ in the "Is Not a Solution" column for $y = -5$ .
\begin{tabular}{|r|r|r|} \cline { 2 - 3 } & Is a Solution & Is Not a Solution \\ \hline-10 & & X \\ \hline-5 & & X \\ \hline 0 & & \\ \hline \end{tabular}

STEP 18

Test $y = 0$ by substituting it into the inequality.
$\frac{2}{5} (0) - 13 > -15$

STEP 19

Calculate the left side of the inequality.
$\frac{2}{5} (0) - 13 = 0 - 13$

STEP 20

Simplify the left side of the inequality.
$0 - 13 = -13$

STEP 21

Compare the calculated value with $-15$ .
$-13 > -15$

STEP 22

Since $-13$ is greater than $-15$ , $y = 0$ is a solution to the inequality. Place an $X$ in the "Is a Solution" column for $y = 0$ .
\begin{tabular}{|r|r|r|} \cline { 2 - 3 } & Is a Solution & Is Not a Solution \\ \hline-10 & & X \\ \hline-5 & & X \\ \hline 0 & X & \\ \hline \end{tabular}
The completed table is:
\begin{tabular}{|r|r|r|} \cline { 2 - 3 } & Is a Solution & Is Not a Solution \\ \hline-10 & & X \\ \hline-5 & & X \\ \hline 0 & X & \\ \hline \end{tabular}

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