Multiple Choice
Verify that the given value is a solution to the equation.
2. Linear Equations and Inequalities
The Addition and Subtraction Properties of Equality
Multiple Choice
Solve the given linear equation using addition and subtraction properties of equality.
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Verified step by step guidance1
Start with the given equation: \(2\left(x+5\right) = 3\left(x-1\right)\).
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. This gives \(2x + 10 = 3x - 3\).
Use the addition or 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: \(10 = 3x - 3 - 2x\).
Simplify the right side by combining like terms: \(10 = x - 3\).
Finally, add 3 to both sides to isolate \(x\): \(10 + 3 = x\), which simplifies to \(x = 13\).
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