Final answer:
To solve for b in the equation 1.8(b - 5.3) - 4.2 = 5.8 (b -2.3), distribute the numbers, combine like terms, move variables to one side, and solve for b to get the approximate solution b ≈ -0.1818.
Step-by-step explanation:
The student is asking for the solution to a linear equation, specifically they want to find the value of b in the equation 1.8(b - 5.3) - 4.2 = 5.8 (b - 2.3). To solve for b, we need to apply the distributive property, combine like terms, and isolate the variable b.
Step-by-step solution
Apply the distributive property: 1.8b - 9.54 - 4.2 = 5.8b - 13.34.
Combine like terms: -9.54 - 4.2 = -13.74 and 5.8b - 1.8b = 4b, resulting in 4b - 13.74 = 1.8b - 13.34.
Move the terms with b on one side and the constants on the other: 4b - 1.8b = 13.34 - 13.74, simplifying to 2.2b = -0.4.
Divide both sides by 2.2 to solve for b: b = -0.4 / 2.2.
Calculate b: b ≈ -0.1818.
The value of b in the given equation is approximately -0.1818.