Solve the System of Inequalities -1+5n>-26 and 7n-2<=12

$- 1 + 5 n > - 26$ and $7 n - 2 \leq 12$

Step 1

Simplify the first inequality.

Move all terms not containing $n$ to the right side of the inequality.

Add $1$ to both sides of the inequality.

$5 n > - 26 + 1$ and $7 n - 2 \leq 12$

Add $- 26$ and $1$ .

$5 n > - 25$ and $7 n - 2 \leq 12$

Divide each term in $5 n > - 25$ by $5$ and simplify.

Divide each term in $5 n > - 25$ by $5$ .

$\frac{5 n}{5} > \frac{- 25}{5}$ and $7 n - 2 \leq 12$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} > \frac{- 25}{5}$ and $7 n - 2 \leq 12$

Divide $n$ by $1$ .

$n > \frac{- 25}{5}$ and $7 n - 2 \leq 12$

Simplify the right side.

Divide $- 25$ by $5$ .

$n > - 5$ and $7 n - 2 \leq 12$

Step 2

Simplify the second inequality.

Move all terms not containing $n$ to the right side of the inequality.

Add $2$ to both sides of the inequality.

$n > - 5$ and $7 n \leq 12 + 2$

Add $12$ and $2$ .

$n > - 5$ and $7 n \leq 14$

Divide each term in $7 n \leq 14$ by $7$ and simplify.

Divide each term in $7 n \leq 14$ by $7$ .

$n > - 5$ and $\frac{7 n}{7} \leq \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$n > - 5$ and $\frac{7 n}{7} \leq \frac{14}{7}$

Divide $n$ by $1$ .

$n > - 5$ and $n \leq \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$n > - 5$ and $n \leq 2$

Step 3

The intersection consists of the elements that are contained in both intervals.

$- 5 < n \leq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 5 < n \leq 2$

Interval Notation:

$(- 5, 2]$

Step 5

Solve the System of Inequalities -1+5n>-26 and 7n-2<=12

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