Question

Consider the sequence of steps to solve the equation:
5(x - 3) =
7x
2


Step 1 ⇒ 10(x - 3) = 7x
Step 2 ⇒ 10x - 30 = 7x
Step 3 ⇒ 3x - 30 = 0
Step 4 ⇒ 3x = 30
Step 5 ⇒ x = 10

Identify the property of equality which yields Step 3.
A) Division Property
B) Addition Property
C) Subtraction Property
D) Multiplication Property

Answer 1

multiplication i think..

Answer 2

$Given \: simple \:equation : \\10(x-3) = 7x$

Step 1:

$10(x-3) = 7x \: (given )$

Step 2:

/* By Distributive Property */

$10x - 30 = 7x$

Step 3:

$\underline {\pink { Subtract\: both\: sides\: by\:<strong> </strong>7x}}\\ <strong>,</strong><strong> </strong>we \:get$

$\implies 10x - 30 - 7x = 7x - 7x$

$\implies 3x - 30 = 0$

Step 4:

/* Adding both sides by 30 , we get */

$\implies 3x - 30 + 30 = 0 + 30$

$\implies 3x = 30$

Step 5:

/* Dividing both sides by 3 , we get */

$\implies \frac{3x}{3} = \frac{30}{3}$

$\implies x = 10$

Therefore.,

$Option \: \green { ( c ) } \: is \: correct$

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