Answer:
m = -1
Step-by-step explanation:
Solve for m:
5 (m - 7) = -8 (3 m + 8)
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
5 m - 35 = -8 (3 m + 8)
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the right hand side:
5 m - 35 = -24 m - 64
Hint: | Move terms with m to the left hand side.
Add 24 m to both sides:
24 m + 5 m - 35 = (24 m - 24 m) - 64
Hint: | Look for the difference of two identical terms.
24 m - 24 m = 0:
24 m + 5 m - 35 = -64
Hint: | Group like terms in 24 m + 5 m - 35.
Grouping like terms, 24 m + 5 m - 35 = (5 m + 24 m) - 35:
(5 m + 24 m) - 35 = -64
Hint: | Add like terms in 5 m + 24 m.
5 m + 24 m = 29 m:
29 m - 35 = -64
Hint: | Isolate terms with m to the left hand side.
Add 35 to both sides:
29 m + (35 - 35) = 35 - 64
Hint: | Look for the difference of two identical terms.
35 - 35 = 0:
29 m = 35 - 64
Hint: | Evaluate 35 - 64.
35 - 64 = -29:
29 m = -29
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 29 m = -29 by 29:
(29 m)/29 = (-29)/29
Hint: | Any nonzero number divided by itself is one.
29/29 = 1:
m = (-29)/29
Hint: | Reduce (-29)/29 to lowest terms. Start by finding the GCD of -29 and 29.
The gcd of -29 and 29 is 29, so (-29)/29 = (29 (-1))/(29×1) = 29/29×-1 = -1:
Answer: m = -1
/6 (when finding the inverse, always take the positive value, ignore the negative sign)