Which pair shows equivalent expressions? 2 x + 10 = negative 2 (x minus 5) Negative 2 (x + 5) = 2 x minus 10 Negative 2 x minus 10 = negative 2 (x + 5) Negative 2 (x minus 5) = negative 2 x minus 10

C. - 2x - 10 = - 2 (x + 5)

Step-by-step explanation:

Clearer choices:

2x + 10 = - 2 (x - 5)

-2 (x + 5) = 2x - 10

-2x - 10 = - 2 (x + 5)

-2 (x - 5) = - 2x - 10

All choices have either:

-2 (x - 5) for A and D

or - 2 (x + 5) for B and C

Simplify these expressions by expanding with the distributive property. Multiply the outside term "-2" with each term inside the brackets.

-2 (x - 5)

= (-2*x) - (-2*5) Multiply each term by the coefficient

= - 2x - (-10) Simplify the double negative to a positive

= - 2x + 10 Expanded expression

This is not the same answer in A and D. They are not correct.

-2 (x + 5)

= (-2*x) + (-2*5) Multiply each term by the coefficient

= - 2x + (-10) Adding a negative is the same as subtraction

= - 2x - 10 Expanded expression

This is the same answer for option C.

Therefore "C" is the answer.

C

Step-by-step explanation:

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