Chapter ISG, Problem 1.1STP

To determine

To calculate the expressions equivalent to the given expression

Answer to Problem 1.1STP

The expressions equivalent to $3x-12y$ are $3(x-4y)$ , $x+4y+2(x-8y)$ and $4(x-3y)-x$

Explanation of Solution

Given information:

The given expression is $3x-12y$

Option 1,

= $4(x-3y)$

Opening the brackets,

= $4x-12y$

Comparing to the given expression.

They are not equivalent.

Option 2,

= $3(x-4y)$

Opening the brackets,

= $3x-12y$

Comparing to the given expression.

They are equivalent.

Option 3,

= $x+4y+2(x-8y)$

Opening the brackets,

= $x+4y+2x-16y$

On solving,

= $3x-12y$

Comparing to the given expression.

They are equivalent

Option 4,

= $2x-6y-(x-6y)$

Opening the brackets,

= $2x-6y-x+6y$

On solving,

= $x$

Comparing to the given expression.

They are not equivalent.

Option 5,

= $6x-6y-(3x-6y)$

Opening the brackets,

= $6x-6y-3x+6y$

On solving,

= $3x$

Comparing to the given expression.

They are not equivalent.

Option 6,

= $4(x-3y)-x$

Opening the brackets,

= $4x-12y-x$

On solving,

= $3x-12y$

Comparing to the given expression,

They are equivalent.