Solve each equation for the variable: (a) x=(212-32)/(1.8) (b) 8.9 (g)/(mL)=(40.90 g)/(x) (c) 7

step 1 In problem set one, we are asked to solve each of the equations that we are given. So I'm first

Solve each equation for the variable: (a) x=(212-32)/(1.8)...

Key Concepts

Linear Equations

Linear equations are mathematical statements of equality that involve a variable raised only to the first power. Solving such equations involves finding the value of the variable that makes the equation true. The process typically requires algebraic manipulation to isolate the variable on one side of the equation using inverse operations.

Inverse Operations

Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division. They are fundamental in solving equations because they allow you to systematically isolate the variable by performing the opposite operation on both sides of the equation, maintaining the equivalence of the equation.

Proportional Reasoning

Proportional reasoning involves understanding and working with ratios and proportions. In equations where one quantity is expressed as a fraction or ratio with an unknown variable, cross multiplication or multiplication by the reciprocal is used to solve for the variable. This concept is crucial for solving problems that compare two ratios or rates.

Arithmetic with Decimals

Arithmetic operations with decimals include addition, subtraction, multiplication, and division involving decimal numbers. Proficiency in handling decimals is essential when solving equations that incorporate decimal coefficients or constants, ensuring accurate manipulation and calculation during the solution process.

Transcript

Please give Ace some feedback