Solve for c: -10 + 3c + 1 = 3 + 5c
Understand the Problem
The question is asking us to solve the equation for the variable c. It involves rearranging the equation to isolate c on one side.
Answer
$c = -6$
Answer for screen readers
The value of $c$ is $-6$.
Steps to Solve
- Combine like terms on the left side
Combine the constants on the left side of the equation: $$ -10 + 1 = -9 $$ So, the equation becomes: $$ -9 + 3c = 3 + 5c $$
- Rearrange the equation to isolate terms with c
Subtract $3c$ from both sides of the equation: $$ -9 = 3 + 5c - 3c $$ This simplifies to: $$ -9 = 3 + 2c $$
- Move the constant to the other side
Subtract 3 from both sides of the equation: $$ -9 - 3 = 2c $$ This simplifies to: $$ -12 = 2c $$
- Solve for c
Divide both sides by 2: $$ c = \frac{-12}{2} $$ So, we have: $$ c = -6 $$
The value of $c$ is $-6$.
More Information
The solution shows how to manipulate the equation by combining like terms and isolating the variable, which is a fundamental concept in algebra.
Tips
- Incorrectly combining constants: Always double-check when combining numbers to ensure accuracy.
- Not isolating variables properly: Ensure to move all terms involving the variable to one side of the equation correctly.
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