Video: Solving Linear Equations Involving Expanding Parentheses

Solve the equation −6(9𝑥 − 2) − 4(7𝑥 + 1) = −5(2𝑥 − 4).

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Video Transcript

Solve the equation negative six multiplied by nine 𝑥 minus two minus four multiplied by seven 𝑥 plus one equals negative five multiplied by two 𝑥 minus four.

Our first step is to multiply the three sets of parentheses. Negative six multiplied by nine 𝑥 is negative 54𝑥, negative six multiplied by negative two is positive 12, negative four multiplied by seven 𝑥 is negative 28𝑥, and negative four multiplied by positive one is negative four. On the other side of the equation, negative five multiplied by two 𝑥 is negative 10𝑥. And finally, negative five multiplied by negative four is positive 20.

Our next step is to group the like terms on the left-hand side. Simplifying here gives us negative 82𝑥 plus eight. We now need to balance the equation, firstly by adding 82𝑥 to both sides of the equation. This leaves us with eight equals 72𝑥 plus 20. We then subtract 20 from both sides of the equation. On the left-hand side, eight minus 20 is negative 12. And on the right-hand side, the 20s cancel leaving us with 72𝑥. Dividing both sides of the equation by 72 gives us an answer of 𝑥 equals minus 12 over 72.

This can be simplified by cancelling the fraction, dividing the top, numerator, and the denominator, the bottom, by 12 gives us a final answer of 𝑥 equals minus one-sixth.

In order to check our answer, we could substitute this value into the initial equation. Substituting 𝑥 equals minus one-sixth, everywhere you see an 𝑥, would ensure that the left-hand side is equal to the right-hand side.

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