Solve for all values of a in simplest form. |-9+5a|=54 Answer: a=

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Solve for all values of  a in simplest form.  |-9+5a|=54 Answer:  a=

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Given Equation: We are given the absolute value equation |-9+5a|=54. The absolute value of a number is the distance of that number from zero on the number line, which means it is always non-negative. Therefore, the expression inside the absolute value can be either positive or negative, and we must consider both cases to solve for a.Case 1: Positive or Zero: First, let's consider the case where the expression inside the absolute value is positive or zero. This means we can remove the absolute value bars without changing the sign: -9+5a = 54 Now, we solve for a by isolating it on one side of the equation.Case 1: Solve for a: Add 9 to both sides of the equation to get: 5a = 54 + 9 5a = 63Case 1: Final Solution: Now, divide both sides by 5 to solve for a: a = 63 / 5 a = 12.6 This is the first solution for a.Case 2: Negative: Next, let's consider the case where the expression inside the absolute value is negative. In this case, we need to consider the equation with the expression inside the absolute value being the opposite sign: -9+5a = -54 Now, we solve for a by isolating it on one side of the equation.Case 2: Solve for a: Add 9 to both sides of the equation to get: 5a = -54 + 9 5a = -45Case 2: Final Solution: Now, divide both sides by 5 to solve for a: a = -45 / 5 a = -9 This is the second solution for a.

Solve for all values of $a$ in simplest form. $\newline$ $|-9+5 a|=54$ $\newline$ Answer: $a=$

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Solve for all values of $a$ in simplest form. $\newline$ $|-9+5 a|=54$ $\newline$ Answer: $a=$