Question

Which expressions are equivalent to 7x – 14? Check all that apply. 14 – 7x x – 2 –(14 – 7x) 7(x – 2) 3x – 14 4x 2x – 10 5x 4.

Answer 1

Linear equation are the equation which has the highest power of the unknown variable is 1.The expressions given in the  option 1, 2, and 3 are equivalent to $7x - 14$.

The equations given in the problem are the linear equations.

Linear equation

Linear equation are the equation which has the highest power of the unknown variable is 1.

Given-

1) The given expression in the problem is,

$f(x)=7x-14$

Rewrite the equation as,

$f(x)=(7x-14)$

Take out the negative sign from the bracket,

$f(x)=-(-7x+14)$

Rewrite the equation with positive terms first.

$f(x)=-(14-7x)$

Hence the given equation is equivalent to the option 1.

2) The given equation,

$f(x)=7x-14$

On solving further take out the 7 common from the bracket,

$f(x)=7(x-2)$

Thus the given equation is equivalent to the option 2.

3) The given equation,

$f(x)=7x-14$

Split the term of x,

$f(x)=4x+3x-14$

Rewrite the equation,

$f(x)=3x-14+4x$

Hence the given equation is equivalent to the option 3.

4) The given equation,

$f(x)=7x-14$

Split the term of x and constant term,

$f(x)=5x+2x-10-4$

Rewrite the equation,

$f(x)=2x-10+5x-4$

Hence the given equation is not equivalent to the option 4.

Thus the expressions given in the  option 1, 2, and 3 are equivalent to $7x - 14$.

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