Solve the Inequality for x 7*|x+2|+5>4

$7 \cdot | x + 2 | + 5 > 4$

Write $7 \cdot | x + 2 | + 5 > 4$ as a piecewise.

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$x + 2 \geq 0$

Subtract $2$ from both sides of the inequality.

$x \geq - 2$

In the piece where $x + 2$ is non-negative, remove the absolute value.

$7 \cdot (x + 2) + 5 > 4$

To find the interval for the second piece, find where the inside of the absolute value is negative.

$x + 2 < 0$

Subtract $2$ from both sides of the inequality.

$x < - 2$

In the piece where $x + 2$ is negative, remove the absolute value and multiply by $- 1$ .

$7 \cdot (- (x + 2)) + 5 > 4$

Write as a piecewise.

${\begin{cases} 7 \cdot (x + 2) + 5 > 4 & x \geq - 2 \\ 7 \cdot (- (x + 2)) + 5 > 4 & x < - 2 \end{cases}$

Simplify $7 \cdot (x + 2) + 5 > 4$ .

Simplify each term.

Apply the distributive property.

${\begin{cases} 7 x + 7 \cdot 2 + 5 > 4 & x \geq - 2 \\ 7 \cdot (- (x + 2)) + 5 > 4 & x < - 2 \end{cases}$

Multiply $7$ by $2$ .

${\begin{cases} 7 x + 14 + 5 > 4 & x \geq - 2 \\ 7 \cdot (- (x + 2)) + 5 > 4 & x < - 2 \end{cases}$

Add $14$ and $5$ .

${\begin{cases} 7 x + 19 > 4 & x \geq - 2 \\ 7 \cdot (- (x + 2)) + 5 > 4 & x < - 2 \end{cases}$

Simplify $7 \cdot (- (x + 2)) + 5 > 4$ .

Simplify each term.

Apply the distributive property.

${\begin{cases} 7 x + 19 > 4 & x \geq - 2 \\ 7 \cdot (- x - 1 \cdot 2) + 5 > 4 & x < - 2 \end{cases}$

Multiply $- 1$ by $2$ .

${\begin{cases} 7 x + 19 > 4 & x \geq - 2 \\ 7 \cdot (- x - 2) + 5 > 4 & x < - 2 \end{cases}$

Apply the distributive property.

${\begin{cases} 7 x + 19 > 4 & x \geq - 2 \\ 7 (- x) + 7 \cdot - 2 + 5 > 4 & x < - 2 \end{cases}$

Multiply $- 1$ by $7$ .

${\begin{cases} 7 x + 19 > 4 & x \geq - 2 \\ - 7 x + 7 \cdot - 2 + 5 > 4 & x < - 2 \end{cases}$

Multiply $7$ by $- 2$ .

${\begin{cases} 7 x + 19 > 4 & x \geq - 2 \\ - 7 x - 14 + 5 > 4 & x < - 2 \end{cases}$

Add $- 14$ and $5$ .

${\begin{cases} 7 x + 19 > 4 & x \geq - 2 \\ - 7 x - 9 > 4 & x < - 2 \end{cases}$

Solve $7 x + 19 > 4$ when $x \geq - 2$ .

Solve $7 x + 19 > 4$ for $x$ .

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

Subtract $19$ from both sides of the inequality.

$7 x > 4 - 19$

Subtract $19$ from $4$ .

$7 x > - 15$

Divide each term in $7 x > - 15$ by $7$ and simplify.

Divide each term in $7 x > - 15$ by $7$ .

$\frac{7 x}{7} > \frac{- 15}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} > \frac{- 15}{7}$

Divide $x$ by $1$ .

$x > \frac{- 15}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{15}{7}$

Find the intersection of $x > - \frac{15}{7}$ and $x \geq - 2$ .

$x \geq - 2$

Solve $- 7 x - 9 > 4$ when $x < - 2$ .

Solve $- 7 x - 9 > 4$ for $x$ .

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

Add $9$ to both sides of the inequality.

$- 7 x > 4 + 9$

Add $4$ and $9$ .

$- 7 x > 13$

Divide each term in $- 7 x > 13$ by $- 7$ and simplify.

Divide each term in $- 7 x > 13$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} < \frac{13}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} < \frac{13}{- 7}$

Divide $x$ by $1$ .

$x < \frac{13}{- 7}$

Simplify the right side.

Move the negative in front of the fraction.

$x < - \frac{13}{7}$

Find the intersection of $x < - \frac{13}{7}$ and $x < - 2$ .

$x < - 2$

Find the union of the solutions.

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Solve the Inequality for x 7*|x+2|+5>4

Related Questions

Support LCMGCF.com by disabling your adblocker.