Answer:
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:
Answer: x = 2
