Question

Help simplify this for me, please! -2(x + 5) + (x - 5) and also, write this equation: The difference of a number and 5 is the opposite of 12.

a) -3x - 5 , x = 7
b) -3x + 5 , x = 7
c) 3x - 5 , x = -7
d) 3x + 5 , x = -7

Answer 1

The simplified expression for -2(x + 5) + (x - 5) is -3x - 5. The correct equation representing "The difference of a number and 5 is the opposite of 12" is -3x - 5, where x = 7. Thus, the correct option is a. -3x - 5 , x = 7.

Step-by-step explanation:

To simplify the expression -2(x + 5) + (x - 5), distribute the coefficients and combine like terms:
`\[-2(x + 5) + (x - 5) = -2x - 10 + x - 5 = -3x - 15\].`Therefore, the simplified expression is -3x - 15. To further simplify it, we can factor out a common factor of 3, resulting in -3(x + 5).

For the equation "The difference of a number and 5 is the opposite of 12," we can represent it algebraically as
`\[x - 5 = -12\]`. Solving for x, we add 5 to both sides:
`\[x = -7\]`. Substituting this value of x into the simplified expression -3x - 15, we get
`\[-3(-7) - 15 = 21 - 15 = 6\].`

`\[-3(-7) - 15 = 21 - 15 = 6\].`

Therefore, the correct option is (a) -3x - 5, and the corresponding value of x is 7. This aligns with the given equation and the simplified expression. The solution satisfies the original equation, confirming its correctness. Thus, the correct option is a. -3x - 5 , x = 7.

Answer 2

The simplified expression is: -2x - 10 + x - 5 = -x - 15

The equation representing "The difference of a number and 5 is the opposite of 12" is:

x - 5 = -12.

Hence all the options a) -3x - 5 , x = 7, b) -3x + 5 , x = 7,c) 3x - 5 , x = -7 and d) 3x + 5 , x = -7 are incorrect.

Explanation:

To simplify the expression -2(x + 5) + (x - 5), apply the distributive property first by multiplying -2 to both terms inside the parentheses: -2 * x = -2x and -2 * 5 = -10. Then, combine the terms with x from the second set of parentheses, resulting in -2x - 10 + x - 5. Combining like terms simplifies this further to -x - 15.

For the equation "The difference of a number and 5 is the opposite of 12," start by defining the difference between a number (let's call it x) and 5 as x - 5. According to the problem, this difference is the opposite of 12, which can be represented as -12. Thus, the equation becomes x - 5 = -12.

Now, solving the equation x - 5 = -12 for x, add 5 to both sides to isolate x. Thus, x = -12 + 5 = -7. Therefore, the value of x satisfying the given equation is x = -7. Comparing this value to the options, we find that the correct answer is option (c) 3x - 5, where x = -7, as it represents the equation x - 5 = -12 when simplified.

Hence all the options a) -3x - 5 , x = 7, b) -3x + 5 , x = 7,c) 3x - 5 , x = -7 and d) 3x + 5 , x = -7 are incorrect.