Respuesta :

Answer:

[tex] \huge \red { \boxed{ \blue{ \boxed{ \tt \: x < - \frac{5}{2} }}}}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • inequality
  • equation
  • PEMDAS

given:

  • [tex] \text{4x + 6 < 2x + 1}[/tex]

to find:

  • [tex] \text{x}[/tex]

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 a negative number
  • Swapping left and right hand sides

let's solve:

[tex]step - 1 : define[/tex]

[tex]4x + 6 < 2x + 1[/tex]

[tex]step - 2 : solve \: for \: x[/tex]

  1. [tex] \tt{cancel \: 6\:from \: both \: sides} \\ \tt{4x + 6 - 6 < 2x + 1 - 6} \\ \tt 4x < 2x - 5[/tex]
  2. [tex] \tt cancel \: 2x \: from \: both \: sides \\ \tt 4x - 2x< 2x - 2x - 5 \\ \tt 2x < - 5[/tex]
  3. [tex] \tt divide \: both \: sides \: by \: 2 \\ \tt\frac{2x}{2} < \frac{ -5 }{2} \\ \tt x < - \frac{5}{2} [/tex]