Question

Choose the missing step in the given solution to the inequality -2x-14>-4+3x

Answer 1

`x \in (-\infty, -2)`

Explanation:

We have to find the solution of the given inequality.

`-2x - 14 > -4 + 3x`

The following steps can be followed to find the solution of the given inequality:

`-2x - 14 > -4 + 3x\\-2x -3x-14 > -4 +3x-3x\\-5x -14 > -4\\-5x -14 +14 > -4 + 14\\-5x > 10\\x < -2\\\text{In interval notation, we can write}\\x \in (-\infty, -2)`

x < -2 is the solution of the given inequality.

Answer 2

`x<-2`

Explanation:

The given inequality is

`-2x-14>-4+3x`

We need to solve the above inequality.

Step 1: Given inequality.

`-2x-14>-4+3x`

Step 2: Add 14 on both sides.

`-2x-14+14>-4+3x+14`

`-2x>10+3x`

Step 3: Subtract 3x from both sides.

`-2x-3x>10+3x-3x`

`-5x>10`

Step 4: Divide both sides by -5. If an inequality is multiplied or divided by a negative number then the sign of inequality will change.

`(-5x)/(-5)<(10)/(-5)`

`x<-2`

Therefore, the solution of given inequality is
`x<-2`.