Try It: Solving and
To practice isolating absolute value expressions with a coefficient, solve the equations and . For the first equation, add to both sides to get , then divide by to find . The equivalent equations are or , which solve to or . For the second equation, subtract from both sides to obtain , then divide by to yield . The equivalent equations or solve to or .
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Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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Try It: Solving and
A quality control analyst uses the equation to determine the upper and lower acceptable size limits for a newly manufactured part. According to the standard procedure for solving this type of equation, what foundational step must the analyst recall and perform before splitting the equation into two separate cases?
A quality control inspector is using the absolute value equation to determine the acceptable length range () for a steel bolt. Arrange the following procedural steps in the correct order to solve for by first isolating the absolute value expression.
An electrical technician uses the equation to determine the acceptable voltage variance () for a specific component. According to the standard algebraic procedure for solving such equations, the technician must first __________ the absolute value expression before it can be rewritten as two separate linear equations.
A quality control technician uses the equation to calculate the pressure tolerance () for a valve. To solve for , the technician must follow a specific sequence of steps to isolate the absolute value expression. Match each equation state with the correct next action required by the standard algebraic procedure.
When an accountant uses an absolute value equation with extra terms to calculate acceptable budget variances, they should immediately split the equation into two separate cases before isolating the absolute value expression.
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In a precision manufacturing facility, a technician uses the equation to determine the acceptable boundary values for a component's length, where represents the length in centimeters. Arrange the following steps in the correct order to solve this equation for .
A logistics coordinator uses the equation to determine the tolerance levels for the weight of shipping containers. According to the standard procedure for solving absolute value equations, which operation should be performed first to begin isolating the absolute value expression?
In a precision logistics facility, technicians use the equation to calibrate weight sensors based on a target value of 5 with a specific tolerance. To maintain quality standards, technicians must follow a Standard Operating Procedure (SOP) to solve this equation. Match each state of the equation with the correct procedural step or result as defined in the SOP.
During a material stress test, an engineer uses the equation to determine the failure points of a composite beam. Following the standard procedure to solve this equation, the engineer first adds 4 to both sides and then divides both sides by 3 to isolate the absolute value expression. After these two steps are performed correctly, the equation simplifies to |x - 4| = ____. (Enter only the numeric value).
When reviewing the standard operating procedure for solving the calibration tolerance equation , the document states that the correct first step to isolate the absolute value expression is to divide both sides of the equation by 3.
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