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What is the expression 4+8(3x−2)−7x

when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.

for 7th grade

1 answer

To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will follow the order of operations (also known as PEMDAS/BODMAS) and apply the distributive property.

  1. Distribute \( 8 \) to both terms inside the parentheses \( (3x - 2) \): \[ 8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16 \]

  2. Substitute this back into the original expression: \[ 4 + (24x - 16) - 7x \]

  3. Now combine like terms. Start with the constants (the numbers) and then the variable terms (the terms with \( x \)):

    • Constants: \( 4 - 16 = -12 \)
    • Variable terms: \( 24x - 7x = 17x \)

  4. Putting it all together: \[ -12 + 17x \]

  5. Rearranging the expression for clarity (usually with the variable first): \[ 17x - 12 \]

So, the expression \( 4 + 8(3x - 2) - 7x \) simplifies to \( \boxed{17x - 12} \).