Fill in the blanks to follow the steps in solving the equation: 5x−12−6x=−10x+7−1

Question

(4 points)
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5x−12−6x=−10x+7−1
Step 1: Combine like terms Response area,

Step 2: Get x-terms on same side of equation Response area

Step 3: Get constants on same side of equation Response area

Step 4: Get the x by itself by using the inverse operation Response area

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Answer 1

To solve the equation \( 5x - 12 - 6x = -10x + 7 - 1 \), we can follow these steps:

Step 1: Combine like terms

• On the left side: \( 5x - 6x = -x \), so it becomes \( -x - 12 \).
• On the right side: \( 7 - 1 = 6 \), so it becomes \( -10x + 6 \).
• Thus, the equation simplifies to: \[ -x - 12 = -10x + 6 \]

Step 2: Get x-terms on the same side of the equation

• Add \( 10x \) to both sides: \[ -x + 10x - 12 = 6 \]
• This simplifies to: \[ 9x - 12 = 6 \]

Step 3: Get constants on the same side of the equation

• Add \( 12 \) to both sides: \[ 9x - 12 + 12 = 6 + 12 \]
• This simplifies to: \[ 9x = 18 \]

Step 4: Get x by itself by using the inverse operation

• Divide both sides by \( 9 \): \[ x = \frac{18}{9} \]
• Thus, \( x = 2 \).

Now, filling in the blanks:

• Step 1: Combine like terms - Combine \(5x\) and \(-6x\) on the left and simplify \(7 - 1\) on the right.
• Step 2: Get x-terms on the same side of the equation - Add \(10x\) to both sides.
• Step 3: Get constants on the same side of the equation - Add \(12\) to both sides.
• Step 4: Get x by itself by using the inverse operation - Divide both sides by \(9\).

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