Which expression is equivalent to 1/2 x + (-70) - 2 1/4 x - (-2)

(-(7 x + 272))/4

Step-by-step explanation:

Simplify the following:

x/2 - (2 + 1/4) x - 70 - ( - 2)

Hint: | Put the fractions in 2 + 1/4 over a common denominator.

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

x/2 - 9/4 x - 70 - ( - 2)

Hint: | Multiply 4 and 2 together.

4×2 = 8:

x/2 - (1/48 + 1/4) x - 70 - ( - 2)

Hint: | Add the fractions over a common denominator to a single fraction.

8/4 + 1/4 = (8 + 1)/4:

x/2 - 9/4 x - 70 - ( - 2)

Hint: | Evaluate 8 + 1.

8 + 1 = 9:

x/2 - 9 x/4 - 70 - ( - 2)

Hint: | Multiply -1 and -2 together.

-(-2) = 2:

x/2 - (9 x)/4 - 70 + 2

Hint: | Put the fractions in x/2 - (9 x)/4 - 70 + 2 over a common denominator.

Put each term in x/2 - (9 x)/4 - 70 + 2 over the common denominator 4: x/2 - (9 x)/4 - 70 + 2 = (2 x)/4 - (9 x)/4 - 280/4 + 8/4:

(2 x)/4 - (9 x)/4 - 280/4 + 8/4

Hint: | Combine (2 x)/4 - (9 x)/4 - 280/4 + 8/4 into a single fraction.

(2 x)/4 - (9 x)/4 - 280/4 + 8/4 = (2 x - 9 x - 280 + 8)/4:

(2 x - 9 x - 280 + 8)/4

Hint: | Group like terms in 2 x - 9 x - 280 + 8.

Grouping like terms, 2 x - 9 x - 280 + 8 = (2 x - 9 x) + (8 - 280):

((2 x - 9 x) + (8 - 280))/4

Hint: | Combine like terms in 2 x - 9 x.

2 x - 9 x = -7 x:

(-7 x + (8 - 280))/4

Hint: | Evaluate 8 - 280.

8 - 280 = -272:

(-272 - 7 x)/4

Hint: | Factor a minus sign out of -7 x - 272.

Factor -1 out of -7 x - 272:

(-(7 x + 272))/4

1/2 x + (-70) - 2 1/4 x - (-2) = (-(7 x + 272))/4 = True