Simplify by combining like terms.
$42.3-8(7-5 n)=-59-40 n$
Answer (2)
To simplify the equation 42.3 − 8 ( 7 − 5 n ) = − 59 − 40 n , we distribute, combine like terms, and isolate n . After following through the steps, we find that n = − 0.56625 . This involves distributing, combining constants, and solving for the variable systematically.
;
Distribute -8 into the parenthesis: 42.3 − 56 + 40 n = − 59 − 40 n .
Combine constant terms: − 13.7 + 40 n = − 59 − 40 n .
Isolate n : 80 n = − 45.3 .
Solve for n : n = − 0.56625 .
Explanation
Understanding the Problem We are given the equation 42.3 − 8 ( 7 − 5 n ) = − 59 − 40 n and we want to simplify it by combining like terms and solve for n .
Distributing First, distribute the -8 into the parenthesis: 42.3 − 8 ( 7 ) − 8 ( − 5 n ) = − 59 − 40 n . This simplifies to 42.3 − 56 + 40 n = − 59 − 40 n .
Combining Constants Next, combine the constant terms on the left side: 42.3 − 56 = − 13.7 , so the equation becomes − 13.7 + 40 n = − 59 − 40 n .
Adding 40n to Both Sides Now, add 40 n to both sides of the equation: − 13.7 + 40 n + 40 n = − 59 − 40 n + 40 n , which simplifies to − 13.7 + 80 n = − 59 .
Adding 13.7 to Both Sides Add 13.7 to both sides: − 13.7 + 80 n + 13.7 = − 59 + 13.7 , which simplifies to 80 n = − 45.3 .
Dividing by 80 Finally, divide both sides by 80: n = 80 − 45.3 . Calculating this gives n = − 0.56625 .
Final Answer Therefore, the solution to the equation is n = − 0.56625 .
Examples
In electrical engineering, simplifying equations by combining like terms is crucial when analyzing circuits. For example, when determining the current in a complex circuit, you might encounter an equation similar to the one we solved. By combining like terms, engineers can simplify the equation to find the unknown current, ensuring the circuit operates as intended. This process is essential for designing and troubleshooting electrical systems efficiently.
