Select all the statements that can be used as steps to solve the equation 6[4(2x−1)]=80−8.
Subtract 8 from 80.
Combine 80 and 6.
Multiply 2x and -1 by 4.
Subtract 1 from both sides of the equation.
Add 4 to both sides of the equation.
Subtract 6 from both sides of the equation.
To solve the equation 6[4(2x−1)]=80−8, we need to simplify both sides of the equation by performing certain steps. Let's analyze the given statements to determine which ones are valid steps for solving the equation:
1. Subtract 8 from 80: This step is not directly related to solving the equation given. It is subtracting numbers on the right side of the equation but doesn't simplify the left side.
2. Combine 80 and 6: Similar to the first statement, this step only combines numbers on the right side of the equation, so it does not help in solving the equation.
3. Multiply 2x and -1 by 4: This step is crucial in simplifying the left side of the equation. By multiplying 2x−1 by 4, we get 8x−4.
4. Subtract 1 from both sides of the equation: This step is also important for simplifying the equation. It allows us to isolate the variable on the left side. We subtract 1 from both sides, resulting in 8x−4=79.
5. Add 4 to both sides of the equation: This statement is not a valid step for solving the given equation. In fact, it would disrupt the equation if we added 4 to both sides of 8x−4=79.
Therefore, the valid steps to solve the equation 6[4(2x−1)]=80−8 are:
- Multiply 2x and -1 by 4: 2x−1 becomes 8x−4.
- Subtract 1 from both sides of the equation: We have 8x−4=79.
Please note that subtracting 6 from both sides of the equation is not necessary for solving this particular equation.