Question
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Answer
\( x = 0 \)
Solution
We are given the equation: 6 – 4x = 7x – 9x + 6
Step 1: Simplify the right side.
Since 7x – 9x = –2x, the equation becomes:
6 – 4x = –2x + 6
Step 2: Eliminate the constant on the right side by subtracting 6 from both sides.
(6 – 4x) – 6 = (–2x + 6) – 6
This simplifies to:
–4x = –2x
Step 3: Isolate x by adding 2x to both sides.
–4x + 2x = –2x + 2x
Which simplifies to:
–2x = 0
Step 4: Solve for x by dividing both sides by –2.
x = 0
Thus, the solution to the equation is x = 0.
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Simplify this solution The Deep Dive
To solve the equation \( 6 - 4x = 7x - 9x + 6 \), we start by simplifying the right side. Combine like terms: \( 7x - 9x \) gives \( -2x \). So, the equation becomes: \( 6 - 4x = -2x + 6 \). Now, let's isolate \( x \) by getting all \( x \) terms on one side and constant terms on the other side. We can subtract \( 6 \) from both sides: \( 6 - 4x - 6 = -2x + 6 - 6 \) This simplifies to: \( -4x = -2x \). Next, add \( 2x \) to both sides: \( -4x + 2x = 0 \), which gives: \( -2x = 0 \). Finally, divide both sides by \( -2 \): \( x = 0 \). So, the solution to the equation is \( x = 0 \).
