Final answer:
To solve the inequality 3v - 8v ≤ -7v + (-28) + (-20) + 10v, we combine like terms to find that v ≤ 6.
Step-by-step explanation:
Combining like terms is a fundamental concept in algebra that involves simplifying expressions by combining terms that have the same variables and exponents. The goal is to make expressions more concise and easier to work with.
The original inequality is 3v - 8v ≤ -7v + (-28) + (-20) + 10v. To solve this, we will combine like terms on each side of the inequality. First, combine the 'v' terms on the left side and the constant terms on the right side:
Left side: 3v - 8v = -5v
Right side: -7v - 28 - 20 = -7v - 48
Now, the inequality looks like this: -5v ≤ 10v - 7v - 48. Continue combining like terms:
-5v ≤ 3v - 48
To isolate 'v', we move all 'v' terms to one side by adding 5v to both sides:
0 ≤ 8v - 48
Finally, divide each side by 8 to solve for 'v':
v ≤ 6