What is the value of x in the equation
2(2x − 5 − 4) = 160 − 17?
A. 40.25
B. 62.25
C. 80.25
D. 143.0
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2(2x − 5 − 4) = 160 − 17
4x - 10 - 8 = 143
4x = 161
x = 40.25
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To solve for the value of x in the equation 2(2x - 5 - 4) = 160 - 17, we can follow these steps:
1. Simplify both sides of the equation by performing any necessary operations within parentheses first.
- On the left side, simplify 2x - 5 - 4 as 2x - 9.
- On the right side, perform the subtraction to get 143.
2. Rewrite the equation with the simplified expressions.
- The equation becomes 2(2x - 9) = 143.
3. Distribute the 2 to the terms inside the parentheses by multiplying.
- Multiply 2 by 2x to get 4x, and multiply 2 by -9 to get -18.
The equation then becomes 4x - 18 = 143.
4. Isolate the term containing x by moving the constant term to the opposite side of the equation.
- Add 18 to both sides to cancel out the -18 on the left side.
- The equation becomes 4x = 161.
5. Solve for x by dividing both sides of the equation by the coefficient of x, which is 4.
- Divide 161 by 4 to get x = 40.25.
Therefore, the value of x in the given equation is 40.25. So, the correct option is A. 40.25.