Solve the given linear equation using addition and subtraction properties of equality.
$2(x+5)=3(x-1)$

• A. $x=-13$
• B. $x=13$
• C. $x=3$
• D. $x=-3$

Answer: (B)

Verified step by step guidance

1. Start with the given equation: \(2\left(x+5\right) = 3\left(x-1\right)\).
2. Apply the distributive property to both sides to eliminate the parentheses: multiply 2 by each term inside the first parentheses and 3 by each term inside the second parentheses, resulting in \$2x + 10 = 3x - 3$.
3. Use the addition and subtraction properties of equality to get all terms containing \(x\) on one side and constants on the other. For example, subtract \$2x\( from both sides to isolate \)x\( terms on one side: \)10 = 3x - 3 - 2x$.
4. Simplify the right side by combining like terms: \$10 = x - 3$.
5. Finally, add 3 to both sides to isolate \(x\): \$10 + 3 = x\(, which simplifies to \)x = 13$.