Solve each equation analytically. Check it analytically, and then support your solution graphic

step 1 The equation is 0 .40 x plus 0 .60 multiplied by 100 minus x equal to 0 .45 multiplied by 100. N

Solve each equation analytically. Check it analytically,...

Key Concepts

Solution Verification

Checking an algebraic solution by substituting it back into the original equation ensures that the derived value satisfies the equation. This step is important to confirm that no errors were made during the manipulation process and that the solution is valid.

Linear Equations

A linear equation is one in which the variable(s) appear only to the first power, and the equation can be written in the form ax + b = c. Solving these equations involves isolating the variable using algebraic operations, which is fundamental in understanding and modeling relationships in many areas of mathematics.

Analytical Solution

Solving an equation analytically means applying algebraic techniques to systematically isolate the variable and determine its exact value. This process typically includes expanding expressions using the distributive property, combining like terms, and performing inverse operations, ensuring a step-by-step solution that can be verified.

Distributive Property

The distributive property allows the multiplication of a single term across terms inside parentheses (i.e., a(b + c) = ab + ac). This property is crucial in expanding and simplifying equations, particularly when dealing with expressions that contain parentheses, as seen in mix or weighted average formulations.

Graphical Verification

Graphical verification involves plotting the functions represented by each side of an equation on a coordinate plane and identifying the point or points where they intersect. This method visually confirms the solution obtained analytically, reinforcing understanding through multiple approaches.

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