Respuesta :

NoblePenguin

Answer:

The final answer is [tex]\bold{x = 5}[/tex].

Step-by-step explanation:

Hey there! We will solve this using the distributive property.

  • The distributive property states that when we are given [tex]a(b \pm c)[/tex], we can "distribute" the a through the parentheses and therefore multiply together a & b as well as a & c.
  • This would end up giving us an equation such as [tex](a \times b \pm b \times c)[/tex].
  • After we get this, we can simplify it as a one-step, two-step, or multi-step equation.

Now, we can apply these methods and solve for x in the equation!

[tex]\text{-7(2 + 2x) = -84 \ \ This is where we begin distributing.}\\\\\text{To distribute, we will multiply the -7 by 2, and the - 7 by 2x.}\\\\\text{Be sure to keep the original operator in the parentheses!}\\\\\text{-14 - 14x = -84 \ \ Now, simplify the equation as a two-step equation.}\\\\\text{-14x = -70 \ \ Now, we have to divide by -14 on both sides to get x by itself.}\\\\\text{x = 5 \ \ And, now, we have our final answer!}[/tex]

And there we go! We found that the final answer is 5. Hope this helps!

Answer:

[tex] \displaystyle \rm \longmapsto \: - 7(2 + 2x) = - 84[/tex]

[tex] \displaystyle \rm \longmapsto \: - 14 + 14x = - 84[/tex]

[tex] \displaystyle \rm \longmapsto \:14x = - 84 + ( - 14)[/tex]

[tex] \displaystyle \rm \longmapsto \:14x =-70 [/tex]

[tex] \displaystyle \rm \longmapsto \:x = \frac{ - 70}{14} [/tex]

[tex] \displaystyle \rm \longmapsto \:x = 5[/tex]

  • For checking:

[tex] \displaystyle \rm \longmapsto \: - 7(2 + 2x) = - 84[/tex]

  • Put x as 5:

[tex] \displaystyle \rm \longmapsto \: - 7(2 + 2(5) = - 84[/tex]

[tex] \displaystyle \rm \longmapsto \: - 7(2 + 10) = - 84[/tex]

[tex] \displaystyle \rm \longmapsto \: - 14 + ( - 70) = - 84[/tex]

[tex] \displaystyle \rm \longmapsto \: - 84 = - 84[/tex]

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