Answer:
x = -8
Step-by-step explanation:
Solve for x:
(3 x)/8 + 6 (x + 3) = 6 x - 5 (x/4 - 1)
Hint: | Put the fractions in x/4 - 1 over a common denominator.
Put each term in x/4 - 1 over the common denominator 4: x/4 - 1 = x/4 - 4/4:
(3 x)/8 + 6 (x + 3) = 6 x - 5 x/4 - 4/4
Hint: | Combine x/4 - 4/4 into a single fraction.
x/4 - 4/4 = (x - 4)/4:
(3 x)/8 + 6 (x + 3) = 6 x - 5(x - 4)/4
Hint: | Put the fractions in (3 x)/8 + 6 (x + 3) over a common denominator.
Put each term in (3 x)/8 + 6 (x + 3) over the common denominator 8: (3 x)/8 + 6 (x + 3) = (3 x)/8 + (48 (x + 3))/8:
(3 x)/8 + (48 (x + 3))/8 = 6 x - (5 (x - 4))/4
Hint: | Combine (3 x)/8 + (48 (x + 3))/8 into a single fraction.
(3 x)/8 + (48 (x + 3))/8 = (3 x + 48 (x + 3))/8:
(3 x + 48 (x + 3))/8 = 6 x - (5 (x - 4))/4
Hint: | Distribute 48 over x + 3.
48 (x + 3) = 48 x + 144:
(48 x + 144 + 3 x)/8 = 6 x - (5 (x - 4))/4
Hint: | Group like terms in 48 x + 3 x + 144.
Grouping like terms, 48 x + 3 x + 144 = (3 x + 48 x) + 144:
((3 x + 48 x) + 144)/8 = 6 x - (5 (x - 4))/4
Hint: | Add like terms in 3 x + 48 x.
3 x + 48 x = 51 x:
(51 x + 144)/8 = 6 x - (5 (x - 4))/4
Hint: | Put the fractions in 6 x - (5 (x - 4))/4 over a common denominator.
Put each term in 6 x - (5 (x - 4))/4 over the common denominator 4: 6 x - (5 (x - 4))/4 = (24 x)/4 - (5 (x - 4))/4:
(51 x + 144)/8 = (24 x)/4 - (5 (x - 4))/4
Hint: | Combine (24 x)/4 - (5 (x - 4))/4 into a single fraction.
(24 x)/4 - (5 (x - 4))/4 = (24 x - 5 (x - 4))/4:
(51 x + 144)/8 = (24 x - 5 (x - 4))/4
Hint: | Distribute -5 over x - 4.
-5 (x - 4) = 20 - 5 x:
(51 x + 144)/8 = (24 x + 20 - 5 x)/4
Hint: | Combine like terms in 24 x - 5 x + 20.
24 x - 5 x = 19 x:
(51 x + 144)/8 = (19 x + 20)/4
Hint: | Make (51 x + 144)/8 = (19 x + 20)/4 simpler by multiplying both sides by a constant.
Multiply both sides by 8:
(8 (51 x + 144))/8 = (8 (19 x + 20))/4
Hint: | Cancel common terms in the numerator and denominator of (8 (51 x + 144))/8.
(8 (51 x + 144))/8 = 8/8×(51 x + 144) = 51 x + 144:
51 x + 144 = (8 (19 x + 20))/4
Hint: | In (8 (19 x + 20))/4, divide 8 in the numerator by 4 in the denominator.
8/4 = (4×2)/4 = 2:
51 x + 144 = 2 (19 x + 20)
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the right hand side:
51 x + 144 = 38 x + 40
Hint: | Move terms with x to the left hand side.
Subtract 38 x from both sides:
(51 x - 38 x) + 144 = (38 x - 38 x) + 40
Hint: | Combine like terms in 51 x - 38 x.
51 x - 38 x = 13 x:
13 x + 144 = (38 x - 38 x) + 40
Hint: | Look for the difference of two identical terms.
38 x - 38 x = 0:
13 x + 144 = 40
Hint: | Isolate terms with x to the left hand side.
Subtract 144 from both sides:
13 x + (144 - 144) = 40 - 144
Hint: | Look for the difference of two identical terms.
144 - 144 = 0:
13 x = 40 - 144
Hint: | Evaluate 40 - 144.
40 - 144 = -104:
13 x = -104
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 13 x = -104 by 13:
(13 x)/13 = (-104)/13
Hint: | Any nonzero number divided by itself is one.
13/13 = 1:
x = (-104)/13
Hint: | Reduce (-104)/13 to lowest terms. Start by finding the GCD of -104 and 13.
The gcd of -104 and 13 is 13, so (-104)/13 = (13 (-8))/(13×1) = 13/13×-8 = -8:
Answer: x = -8
