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

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

Step 1

Simplify the first inequality.

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

Add $91$ to both sides of the inequality.

$3 x > - 87 + 91$ and $17 x - 16 > 18$

Add $- 87$ and $91$ .

$3 x > 4$ and $17 x - 16 > 18$

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

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

$\frac{3 x}{3} > \frac{4}{3}$ and $17 x - 16 > 18$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{4}{3}$ and $17 x - 16 > 18$

Divide $x$ by $1$ .

$x > \frac{4}{3}$ and $17 x - 16 > 18$

Step 2

Simplify the second inequality.

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

Add $16$ to both sides of the inequality.

$x > \frac{4}{3}$ and $17 x > 18 + 16$

Add $18$ and $16$ .

$x > \frac{4}{3}$ and $17 x > 34$

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

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

$x > \frac{4}{3}$ and $\frac{17 x}{17} > \frac{34}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$x > \frac{4}{3}$ and $\frac{17 x}{17} > \frac{34}{17}$

Divide $x$ by $1$ .

$x > \frac{4}{3}$ and $x > \frac{34}{17}$

Simplify the right side.

Divide $34$ by $17$ .

$x > \frac{4}{3}$ and $x > 2$

Step 3

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

$x > 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$

Step 5

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

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