To solve the equation \(5 - 3 (x + 3) = 11 - 8x\), we can identify the properties and steps used to arrive at the solution.
-
Distributive Property: This property is used to eliminate the parentheses by distributing the \(-3\) across \((x + 3)\). \[ 5 - 3x - 9 = 11 - 8x \]
-
Combining Like Terms: After applying the distributive property, we combine like terms on the left side. \[ 5 - 9 - 3x = 11 - 8x \implies -4 - 3x = 11 - 8x \]
-
Adding/Subtracting Terms: We can add \(8x\) and \(4\) to both sides to isolate \(x\). \[ -3x + 8x = 11 + 4 \implies 5x = 15 \]
-
Division Property of Equality: Divide by \(5\) to solve for \(x\). \[ x = 3 \]
So overall, the properties used include the Distributive Property, Combining Like Terms, and the Addition/Subtraction Property of Equality followed by the Division Property of Equality.
The related intermediate steps and results show the following equations:
- \(5 - 3(x + 3) = 11 - 8x\) ➔ Original Equation
- \(5 - 3x - 9 = 11 - 8x\) ➔ Distributing and combining
- \(-3x - 4 = 11 - 8x\) ➔ Rearranging terms
- \(5x - 4 = 11\) ➔ Simplifying
- \(5x = 15\) ➔ Isolating variable
- \(x = 3\) ➔ Final solution
These steps reflect the algebraic manipulations and properties used to solve the equation.