Question

Determine o valor x da equação (2+3)+ (2x+7)+ (2x+11)+..+(2x+79)=1100

Answer 1

Resposta:

$\left(2+3\right)+\left(2x+7\right)+\left(2x+11\right)+\left(2x+79\right)=1100\quad :\quad x=\frac{499}{3}$

$\left(\mathrm{Decimal}:\quad x=166.33333\dots \right)$

Explicação passo a passo:

$Passos\\\left(2+3\right)+\left(2x+7\right)+\left(2x+11\right)+\left(2x+79\right)=1100$

Remover os parênteses: $\left(a\right)=a$

$2+3+2x+7+2x+11+2x+79=1100$

$\mathrm{Agrupar\:termos\:semelhantes}$

$2x+2x+2x+2+3+7+11+79=1100$

$Somar\:elementos\:similares: 2x+2x+2x=6x\\6x+2+3+7+11+79=1100$

$\mathrm{Somar:}\:2+3+7+11+79=102\\6x+102=1100$

$\mathrm{Subtrair\:}102\mathrm{\:de\:ambos\:os\:lados}\\6x+102-102=1100-102$

$\mathrm{Simplificar}\\6x=998$

$\mathrm{Dividir\:ambos\:os\:lados\:por\:}6\\\frac{6x}{6}=\frac{998}{6}$

$\mathrm{Simplificar}\\x=\frac{499}{3}$

Grafico