Answer:
a = 8/29 thus: Step 1 is wrong!
Explanation:
Solve for a:
8 - a/2 = 3 (4 - 5 a)
Hint: | Put the fractions in 8 - a/2 over a common denominator.
Put each term in 8 - a/2 over the common denominator 2: 8 - a/2 = 16/2 - a/2:
16/2 - a/2 = 3 (4 - 5 a)
Hint: | Combine 16/2 - a/2 into a single fraction.
16/2 - a/2 = (16 - a)/2:
(16 - a)/2 = 3 (4 - 5 a)
Hint: | Make (16 - a)/2 = 3 (4 - 5 a) simpler by multiplying both sides by a constant.
Multiply both sides by 2:
(2 (16 - a))/2 = 2×3 (4 - 5 a)
Hint: | Cancel common terms in the numerator and denominator of (2 (16 - a))/2.
(2 (16 - a))/2 = 2/2×(16 - a) = 16 - a:
16 - a = 2×3 (4 - 5 a)
Hint: | Multiply 2 and 3 together.
2×3 = 6:
16 - a = 6 (4 - 5 a)
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the right hand side:
16 - a = 24 - 30 a
Hint: | Move terms with a to the left hand side.
Add 30 a to both sides:
30 a - a + 16 = (30 a - 30 a) + 24
Hint: | Look for the difference of two identical terms.
30 a - 30 a = 0:
30 a - a + 16 = 24
Hint: | Group like terms in 30 a - a + 16.
Grouping like terms, 30 a - a + 16 = (-a + 30 a) + 16:
(-a + 30 a) + 16 = 24
Hint: | Combine like terms in 30 a - a.
30 a - a = 29 a:
29 a + 16 = 24
Hint: | Isolate terms with a to the left hand side.
Subtract 16 from both sides:
29 a + (16 - 16) = 24 - 16
Hint: | Look for the difference of two identical terms.
16 - 16 = 0:
29 a = 24 - 16
Hint: | Evaluate 24 - 16.
24 - 16 = 8:
29 a = 8
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 29 a = 8 by 29:
(29 a)/29 = 8/29
Hint: | Any nonzero number divided by itself is one.
29/29 = 1:
Answer: a = 8/29