Solve the System of @WORD 4x+2>14-21x+1>22

$4 x + 2 > 14 - 21 x + 1 > 22$

Step 1

Solve $4 x + 2 > 14 - 21 x + 1$ for $x$ .

Add $14$ and $1$ .

$4 x + 2 > - 21 x + 15$

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

Add $21 x$ to both sides of the inequality.

$4 x + 2 + 21 x > 15$

Add $4 x$ and $21 x$ .

$25 x + 2 > 15$

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

Subtract $2$ from both sides of the inequality.

$25 x > 15 - 2$

Subtract $2$ from $15$ .

$25 x > 13$

Divide each term in $25 x > 13$ by $25$ and simplify.

Divide each term in $25 x > 13$ by $25$ .

$\frac{25 x}{25} > \frac{13}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x}{25} > \frac{13}{25}$

Divide $x$ by $1$ .

$x > \frac{13}{25}$

Step 2

Solve $14 - 21 x + 1 > 22$ for $x$ .

Add $14$ and $1$ .

$- 21 x + 15 > 22$

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

Subtract $15$ from both sides of the inequality.

$- 21 x > 22 - 15$

Subtract $15$ from $22$ .

$- 21 x > 7$

Divide each term in $- 21 x > 7$ by $- 21$ and simplify.

Divide each term in $- 21 x > 7$ by $- 21$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 21 x}{- 21} < \frac{7}{- 21}$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 x}{- 21} < \frac{7}{- 21}$

Divide $x$ by $1$ .

$x < \frac{7}{- 21}$

Simplify the right side.

Cancel the common factor of $7$ and $- 21$ .

Factor $7$ out of $7$ .

$x < \frac{7 (1)}{- 21}$

Cancel the common factors.

Factor $7$ out of $- 21$ .

$x < \frac{7 \cdot 1}{7 \cdot - 3}$

Cancel the common factor.

$x < \frac{7 \cdot 1}{7 \cdot - 3}$

Rewrite the expression.

$x < \frac{1}{- 3}$

Move the negative in front of the fraction.

$x < - \frac{1}{3}$

Step 3

Find the intersection of $x > \frac{13}{25}$ and $x < - \frac{1}{3}$ .

No solution

Solve the System of @WORD 4x+2>14-21x+1>22

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