Question

Solucione as equações abaixo:

Answer 1

Explicação passo-a-passo:

a) $\dfrac{5x}{7}-3=\dfrac{2x}{7}+6$

$\dfrac{5x}{7}-\dfrac{2x}{7}=6+3$

$\dfrac{3x}{7}=9$

$3x=9\cdot7$

$3x=63$

$x=\dfrac{63}{3}$

$\boxed{x=21}$

b) $\dfrac{3x}{4}+2=\dfrac{x}{4}-9$

$\dfrac{3x}{4}-\dfrac{x}{4}=-9-2$

$\dfrac{2x}{4}=-11$

$\dfrac{x}{2}=-11$

$x=2\cdot(-11)$

$\boxed{x=-22}$

c) $\dfrac{4x}{5}-8=14x-16$

$14x-\dfrac{4x}{5}=-8+16$

$14x-\dfrac{4x}{5}=8$

$5\cdot14x-4x=5\cdot8$

$70x-4x=40$

$66x=40$

$x=\dfrac{40}{66}$

$\boxed{x=\dfrac{20}{33}}$

d) $\dfrac{3x}{4}-6=6-x$

$\dfrac{3x}{4}+x=6+6$

$\dfrac{3x}{4}+x=12$

$3x+4x=4\cdot12$

$7x=48$

$\boxed{x=\dfrac{48}{7}}$

e) $\dfrac{5x}{6}-\dfrac{3x}{4}=1$

$\dfrac{2\cdot5x-3\cdot3x}{12}=1$

$\dfrac{10x-9x}{12}=1$

$\dfrac{x}{12}=1$

$x=12\cdot1$

$\boxed{x=12}$

f) $\dfrac{5\cdot(x-12)}{4}=3\cdot(2x-7)$

$5\cdot(x-12)=4\cdot3\cdot(2x-7)$

$5x-60=12\cdot(2x-7)$

$5x-60=24x-84$

$24x-5x=84-60$

$19x=24$

$\boxed{x=\dfrac{24}{19}}$