Solve the System of Inequalities 3x-91>-87 AND 17x-16>18

$3 x - 91 > - 87$ AND $17 x - 16 > 18$

Step 1

Solve $3 x - 91 > - 87$ for $x$ .

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

Add $91$ to both sides of the inequality.

$3 x > - 87 + 91$

Add $- 87$ and $91$ .

$3 x > 4$

Divide each term in $3 x > 4$ by $3$ and simplify.

Divide each term in $3 x > 4$ by $3$ .

$\frac{3 x}{3} > \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{4}{3}$

Divide $x$ by $1$ .

$x > \frac{4}{3}$

Step 2

Solve $17 x - 16 > 18$ for $x$ .

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

Add $16$ to both sides of the inequality.

$17 x > 18 + 16$

Add $18$ and $16$ .

$17 x > 34$

Divide each term in $17 x > 34$ by $17$ and simplify.

Divide each term in $17 x > 34$ by $17$ .

$\frac{17 x}{17} > \frac{34}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 x}{17} > \frac{34}{17}$

Divide $x$ by $1$ .

$x > \frac{34}{17}$

Simplify the right side.

Divide $34$ by $17$ .

$x > 2$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$

Step 4