2(5v + 3) - 4(7v + 1) = -88
Understand the Problem
The question is asking to solve the equation involving the variable v. It requires distribution, combining like terms, and isolating v on one side of the equation.
Answer
The final answer is \( v = 5 \).
Answer for screen readers
The solution to the equation is ( v = 5 ).
Steps to Solve
- Distribute the Terms Begin by distributing the constants through the parentheses: $$ 2(5v + 3) = 10v + 6 $$ $$ -4(7v + 1) = -28v - 4 $$
Combining these, we have: $$ 10v + 6 - 28v - 4 = -88 $$
-
Combine Like Terms Now, combine the like terms on the left side: $$ (10v - 28v) + (6 - 4) = -88 $$ This simplifies to: $$ -18v + 2 = -88 $$
-
Isolate the Variable Next, subtract 2 from both sides to isolate the term with $v$: $$ -18v = -88 - 2 $$ $$ -18v = -90 $$
-
Solve for v Finally, divide both sides by -18: $$ v = \frac{-90}{-18} $$ Simplifying this gives: $$ v = 5 $$
The solution to the equation is ( v = 5 ).
More Information
This equation illustrates the importance of distributing terms and combining like terms, which are fundamental skills in algebra.
Tips
- Not distributing correctly: It's easy to forget to apply the negative sign when distributing, particularly with the second term.
- Combining constants incorrectly: Ensure that constants are correctly added or subtracted when combining like terms.
AI-generated content may contain errors. Please verify critical information
