Question

1.8(b−5.3)−4.2=5.8(b−2.3). Determine the value of b.

Answer 1

To solve the equation 1.8(b−5.3)−4.2=5.8(b−2.3) and determine the value of b, follow these steps: distribute, simplify, combine like terms, isolate the variable, and calculate the value of b. The value of b in the equation is -0.1.

Step-by-step explanation:

To solve the equation 1.8(b−5.3)−4.2=5.8(b−2.3) and determine the value of b, we need to simplify and isolate the variable. Here are the steps:

1. Distribute 1.8 to both terms inside the parentheses: 1.8b - 1.8(5.3) - 4.2 = 5.8b - 5.8(2.3).
2. Perform the multiplication: 1.8b - 9.54 - 4.2 = 5.8b - 13.34.
3. Combine like terms: 1.8b - 13.74 = 5.8b - 13.34.
4. Group the variable terms on one side and the constant terms on the other side: 1.8b - 5.8b = -13.34 + 13.74.
5. Perform the subtraction: -4b = 0.4.
6. Isolate the variable b by dividing both sides of the equation by -4: b = 0.4/-4.
7. Calculate the value of b: b = -0.1.

Therefore, the value of b in the equation 1.8(b−5.3)−4.2=5.8(b−2.3) is -0.1.