Solve the System of Inequalities 3x-18<4x-23 and x-16<-22

$3 x - 18 < 4 x - 23$ and $x - 16 < - 22$

Step 1

Simplify the first inequality.

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

Subtract $4 x$ from both sides of the inequality.

$3 x - 18 - 4 x < - 23$ and $x - 16 < - 22$

Subtract $4 x$ from $3 x$ .

$- x - 18 < - 23$ and $x - 16 < - 22$

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

Add $18$ to both sides of the inequality.

$- x < - 23 + 18$ and $x - 16 < - 22$

Add $- 23$ and $18$ .

$- x < - 5$ and $x - 16 < - 22$

Divide each term in $- x < - 5$ by $- 1$ and simplify.

Divide each term in $- x < - 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 5}{- 1}$ and $x - 16 < - 22$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 5}{- 1}$ and $x - 16 < - 22$

Divide $x$ by $1$ .

$x > \frac{- 5}{- 1}$ and $x - 16 < - 22$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x > 5$ and $x - 16 < - 22$

Step 2

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

Add $16$ to both sides of the inequality.

$x > 5$ and $x < - 22 + 16$

Add $- 22$ and $16$ .

$x > 5$ and $x < - 6$

Step 3

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

No solution

Solve the System of Inequalities 3x-18<4x-23 and x-16<-22

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