Question: For each expression, select all equivalent expressions from the list. (a) \(3x + 12\) - \(3…

For each expression, select all equivalent expressions from the list.

(a) \(3x + 12\)

• \(3 \cdot x + 3 \cdot 4\)
• \(3(x + 4)\)
• \(3(4x + 1)\)
• \(15x\)

(b) \(11 + 16y - 8 - y\)

• \(3y + 15y\)
• \(15 + 3y\)
• \(3y + 15\)
• \(15y + 3\)

Solution

For each expression, we will find the equivalent algebraic expressions. (a) \(3x + 12\) Expanding and simplifying all options: 1. \(3 \cdot x + 3 \cdot 4\) \[ 3x + 12 \] This is equivalent. 2. \(3(x + 4)\) \[ 3x + 12 \] This is equivalent. 3. \(3(4x + 1)\) \[ 12x + 3 \] This is not equivalent. 4. \(15x\) This is not equivalent. (b) \(11 + 16y - 8 - y\) Simplifying the expression: \[ 11 + 16y - 8 - y = 3 + 15y \] Expanding and simplifying all options: 1. \(3y + 15y\) \[ 18y \] This is not equivalent. 2. \(15 + 3y\) This is equivalent. 3. \(3y + 15\) This is equivalent. 4. \(15y + 3\) This is equivalent. Final equivalent expressions: (a) \(3 \cdot x + 3 \cdot 4\), \(3(x + 4)\) (b) \(15 + 3y\), \(3y + 15\), \(15y + 3\)