Question

from unit 4, lesson 6
select all the equations that are equivalent to the equation ( 3x - 4 = 5 ).
a ( 3x = 9 )
b ( 3x - 4 + 4 = 5 + 4 )
c ( x - 4 = 2 )
d ( x = 9 )
e ( -4 = 5 - 3x )

Explanation:

Step1: Analyze original equation

Original equation: $3x - 4 = 5$

Step2: Check Option A

Add 4 to both sides:
$3x - 4 + 4 = 5 + 4$
$3x = 9$
This matches Option A.

Step3: Check Option B

Show the step of adding 4 to both sides:
$3x - 4 + 4 = 5 + 4$
This is exactly Option B.

Step4: Check Option C

Divide original equation by 3:
$\frac{3x - 4}{3} = \frac{5}{3}$
$x - \frac{4}{3} = \frac{5}{3}$, which does not match $x - 4 = 2$.

Step5: Check Option D

From $3x=9$, solve for $x$:
$x = \frac{9}{3} = 3$, which does not match $x=9$.

Step6: Check Option E

Subtract $3x$ from both sides of original equation:
$3x - 4 - 3x = 5 - 3x$
$-4 = 5 - 3x$
This matches Option E.

Answer:

A. $3x = 9$
B. $3x - 4 + 4 = 5 + 4$
E. $-4 = 5 - 3x$