Question

Determine o Valor de X na equação a seguir.
Conta completa pfv

a)
$\frac{3x}{2}$ - 5 = $\frac{x}{4}$

b)
$\frac{x}{2}$ + 5 = $\frac{2x}{3}$ - x

c)
$\frac{x}{3}$ + (x - 2) = $\frac{x}{2}$ + (x - 3)

Answer 1

Resposta:

OLÁ

VAMOS A SUA PERGUNTA:⇒⇒

A:)→

$\sf\dfrac{3x}{2}-5= \dfrac{x}{4}$

$\sf2\times3x-20=x$

$\sf 6x-20=x$

$\sf 6x-20-x=0$

$\sf 5x-20=0$

$\sf 5x=20$

$\sf$$\sf x=\dfrac{20}{5}$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \red{x=4}}}}\ \checkmark$

B:)→

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

$\sf3x+30=2\times2x-6x$

$\sf 3x+30=4x-6x$

$\sf 3x+30=-2x$

$\sf 3x+30+2x=0$

$\sf 5x+30=0$

$\sf 5x=-30$

$\sf x=\dfrac{-30}{5}$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \green{x=-6}}}}\ \checkmark$

C:)→

$\sf \dfrac{x}{3}+(x-2)= \dfrac{x}{2}+(x-3)$

$\sf 2x+6x-12=3x+6x-18$

$\sf 8x-12=3x+6x-18$

$\sf 8x-12=9x-18$

$\sf 8x-12-9x=-18$

$\sf -x-12=-18$

$\sf -x=-18+12$

$\sf -x=-6$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \orange{x=6}}}}\ \checkmark$

Explicação passo-a-passo:

ESPERO TER AJUDADO

Answer 2

Resposta:

a) x=4

b) x= -6

c) x= 6

Explicação passo-a-passo:

a)

$\frac{3x}{2} - 5 = \frac{x}{4} \\ 4( \frac{3x}{2} - 5) = 4 \times 5 = x \\ 2 \times 3x - 20 = x \\ 6x - 20 = x \\6x - x = 20 \\ 5x = 2 \\ x = \frac{20}{5 } \\ x = 4$

b)

$\frac{ x }{2} + 5 = \frac{2}{x} - x \\ 3x + 30 = 4x - 6x \\ 3x + 30 = - 2x \\ 3x + 2x = - 30 \\ 5x = - 30 \\ x = \frac{ - 30}{5} \\ x = - 6$

c)

$\frac{x}{3} + (x - 2) = \frac{x}{2} + (x - 3) \\ \frac{x}{3} + x - 2 = \frac{x}{2} + x - 3 \\ \frac{x}{3} - 2 = \frac{x}{2} - 3 \\ 2x - 12 = 3x - 18 \\ 2x - 3x = - 18 + 12 \\ - x = - 6 \\ x = 6$