Solve the System of @WORD 4x-18<2-17x-8>=-25

$4 x - 18 < 2 - 17 x - 8 \geq - 25$

Step 1

Solve $4 x - 18 < 2 - 17 x - 8$ for $x$ .

Subtract $8$ from $2$ .

$4 x - 18 < - 17 x - 6$

Move all terms containing $x$ to the left side of the inequality.

Add $17 x$ to both sides of the inequality.

$4 x - 18 + 17 x < - 6$

Add $4 x$ and $17 x$ .

$21 x - 18 < - 6$

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

Add $18$ to both sides of the inequality.

$21 x < - 6 + 18$

Add $- 6$ and $18$ .

$21 x < 12$

Divide each term in $21 x < 12$ by $21$ and simplify.

Divide each term in $21 x < 12$ by $21$ .

$\frac{21 x}{21} < \frac{12}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 x}{21} < \frac{12}{21}$

Divide $x$ by $1$ .

$x < \frac{12}{21}$

Simplify the right side.

Cancel the common factor of $12$ and $21$ .

Factor $3$ out of $12$ .

$x < \frac{3 (4)}{21}$

Cancel the common factors.

Factor $3$ out of $21$ .

$x < \frac{3 \cdot 4}{3 \cdot 7}$

Cancel the common factor.

$x < \frac{3 \cdot 4}{3 \cdot 7}$

Rewrite the expression.

$x < \frac{4}{7}$

Step 2

Solve $2 - 17 x - 8 \geq - 25$ for $x$ .

Subtract $8$ from $2$ .

$- 17 x - 6 \geq - 25$

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

Add $6$ to both sides of the inequality.

$- 17 x \geq - 25 + 6$

Add $- 25$ and $6$ .

$- 17 x \geq - 19$

Divide each term in $- 17 x \geq - 19$ by $- 17$ and simplify.

Divide each term in $- 17 x \geq - 19$ by $- 17$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 17 x}{- 17} \leq \frac{- 19}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 x}{- 17} \leq \frac{- 19}{- 17}$

Divide $x$ by $1$ .

$x \leq \frac{- 19}{- 17}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \leq \frac{19}{17}$

Step 3

Find the intersection of $x < \frac{4}{7}$ and $x \leq \frac{19}{17}$ .

$x < \frac{4}{7}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{4}{7}$

Interval Notation:

$(- \infty, \frac{4}{7})$

Step 5

Solve the System of @WORD 4x-18<2-17x-8>=-25

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