Solving
To solve the linear equation , begin by applying the distributive property to the left side, yielding . Next, combine the like decimal variable terms to obtain . Isolate the variable term by subtracting from both sides, which results in . Finally, divide both sides by the coefficient to find the solution, . Another valid approach is to clear the decimals immediately by multiplying every term in the equation by , producing , which will give the same result.
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Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
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Solving
Solving by Clearing Decimals
A logistics coordinator is using the equation to determine a shipping surcharge based on weight. According to the standard strategy for clearing decimals to work with integer coefficients, what value should both sides of the equation be multiplied by?
A corporate accountant is verifying an expense report using a linear equation with decimal coefficients, such as . To apply the standard strategy for clearing these decimals and converting them to integer coefficients, the accountant must multiply both sides of the equation by the corresponding power of ____.
An operations manager is solving a budget equation, such as , to determine a project's variable costs. Arrange the following steps in the correct sequence to solve for using the standard strategy for clearing decimals.
In professional finance and accounting, linear equations are often used to model budget projections and tax rates. When these equations contain decimal coefficients, a common strategy is to clear the decimals by multiplying both sides by a specific power of ten. Match each coefficient scenario with the correct power of ten required to convert that coefficient into an integer.
An accountant is solving a linear equation that includes decimal coefficients, such as . True or False: According to the standard strategy for clearing decimals, the accountant should multiply both sides of the equation by a power of ten determined by the coefficient with the fewest decimal places.
Learn After
A retail manager uses the linear equation to calculate the cost of two different batches of inventory. According to the standard algebraic procedure for solving this equation, which of the following represents the equation immediately after the distributive property has been correctly applied to the term on the left side?
A logistics supervisor is training a new inventory clerk on calculating material costs. They need to solve the equation to determine the base price of a specific packaging material. Arrange the following standard algebraic steps in the correct chronological order to solve the equation.
A production supervisor is calculating the total hours () needed for a specific project using the cost-allocation equation . Based on the standard algebraic procedure described in your training, match each step of the solution process with the correct mathematical expression it produces.
A facilities manager uses the linear equation to determine the hourly rate () for a maintenance contract. To simplify the calculation by 'clearing the decimals' in a single step before solving, the manager should multiply every term in the equation by the number ____.
Simplifying Decimal Coefficients