What are the solution(s) of
of -1/2x+4 = x+1

x=2

Step-by-step explanation:

Solve for x:

4 - x/2 = x + 1

Hint: | Put the fractions in 4 - x/2 over a common denominator.

Put each term in 4 - x/2 over the common denominator 2: 4 - x/2 = 8/2 - x/2:

8/2 - x/2 = x + 1

Hint: | Combine 8/2 - x/2 into a single fraction.

8/2 - x/2 = (8 - x)/2:

(8 - x)/2 = x + 1

Hint: | Make (8 - x)/2 = x + 1 simpler by multiplying both sides by a constant.

Multiply both sides by 2:

(2 (8 - x))/2 = 2 (x + 1)

Hint: | Cancel common terms in the numerator and denominator of (2 (8 - x))/2.

(2 (8 - x))/2 = 2/2×(8 - x) = 8 - x:

8 - x = 2 (x + 1)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

8 - x = 2 x + 2

Hint: | Move terms with x to the left hand side.

Subtract 2 x from both sides:

8 + (-x - 2 x) = (2 x - 2 x) + 2

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

-x - 2 x = -3 x:

-3 x + 8 = (2 x - 2 x) + 2

Hint: | Look for the difference of two identical terms.

2 x - 2 x = 0:

8 - 3 x = 2

Hint: | Isolate terms with x to the left hand side.

Subtract 8 from both sides:

(8 - 8) - 3 x = 2 - 8

Hint: | Look for the difference of two identical terms.

8 - 8 = 0:

-3 x = 2 - 8

Hint: | Evaluate 2 - 8.

2 - 8 = -6:

-3 x = -6

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -3 x = -6 by -3:

(-3 x)/(-3) = (-6)/(-3)

Hint: | Any nonzero number divided by itself is one.

(-3)/(-3) = 1:

x = (-6)/(-3)

Hint: | Reduce (-6)/(-3) to lowest terms. Start by finding the GCD of -6 and -3.

The gcd of -6 and -3 is -3, so (-6)/(-3) = (-3×2)/(-3×1) = (-3)/(-3)×2 = 2:

x = 2

answer: d. $20

step-by-step explanation:

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