Question

Solve for x: 5<-4x-11<13​

Answer 1

-4>x>-6

Explanation:

to understand this

you need to know about:

• inequality
• PEMDAS

tips and formulas:

the direction of inequality does not change when you

• add or subtract a number from both sides
• multiply or divide both sides by a positive number
• simplify a side

the direction of inequality does change when you

• multiply or divide both sides by negative number
• swapping left and right hand side

let's solve:

`\sf 5 < - 4x - 11 < 13`

`step - 2 : solve`

1. 
   `\sf add \: 11 \: to \: every \: sides : \\ \sf 5 + 11 < - 4x - 11 + 11 < 13 + 11 \\ \sf16 < - 4x < 24`
2. 
   `\sf \: divide \: both \: sides \: by \: - 4 \: and \: swap \: the \: inequalities : \\ \sf \sf - 4 > x > - 6`

Answer 2

`- {4} < x < - 6 \\`

Explanation:

`5 < - 4x - 11 < 13`

Add 11 to both sides of the inequality to make - 4x stand alone

`5 + 11 < - 4x - 11 + 11 < 13 + 11 \\ 16 < - 4x < 24`

Divide both sides by - 4

`- (16)/(4) < ( - 4x)/( - 4) < - (24)/(4) \\ - {4} < x < - 6`

Reverse the signs

We have the final answer as

`- 4 > x > - 6 \\`

Hope this helps you