Solve each equation using simplification techniques. Round answers to two decimal places as necessary.
$-27 A+28+29 A=-45$
Answer (1)
Combine like terms: − 27 A + 29 A = 2 A , resulting in 2 A + 28 = − 45 .
Isolate the variable term: Subtract 28 from both sides to get 2 A = − 73 .
Solve for A: Divide both sides by 2, yielding A = − 36.5 .
Round to two decimal places: A = − 36.50 .
Explanation
Problem Analysis We are given the equation − 27 A + 28 + 29 A = − 45 . Our goal is to solve for A .
Combining Like Terms First, we combine the terms with A on the left side of the equation: − 27 A + 29 A = 2 A . So the equation becomes 2 A + 28 = − 45 .
Isolating the Variable Term Next, we want to isolate the term with A . To do this, we subtract 28 from both sides of the equation: 2 A + 28 − 28 = − 45 − 28 , which simplifies to 2 A = − 73 .
Solving for A Now, we solve for A by dividing both sides of the equation by 2: 2 2 A = 2 − 73 , which gives us A = − 36.5 .
Rounding to Two Decimal Places Since we need to round the answer to two decimal places, we have A = − 36.50 .
Final Answer Therefore, the solution to the equation is A = − 36.50 .
Examples
Imagine you are managing a budget where 'A' represents a variable expense. This equation helps you determine the exact value of that expense needed to balance your budget to a specific target. For instance, if you initially thought 'A' was different, solving this equation tells you the precise adjustment needed to meet your financial goals. This type of problem is a fundamental application of algebra in personal finance and business management, ensuring accurate financial planning and control.
