Solve the equation for all values of x. |4x+9|=5x Answer: x=

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Solve the equation for all values of  x.  |4x+9|=5x Answer:  x=

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Consider Two Cases: We have the equation |4x + 9| = 5x. To solve this, we need to consider two cases because the absolute value function outputs the same value for both the positive and negative versions of its input.Case 1: Non-Negative Expression: Case 1: The expression inside the absolute value is non-negative. This means we can remove the absolute value without changing the sign. So, we have 4x + 9 = 5x. Now, we solve for x. Subtract 4x from both sides to get 9 = x.Case 2: Negative Expression: Case 2: The expression inside the absolute value is negative. This means we need to take the negative of the inside expression when removing the absolute value. So, we have -(4x + 9) = 5x. Now, we solve for x. Distribute the negative sign to get -4x - 9 = 5x. Add 4x to both sides to get -9 = 9x. Divide both sides by 9 to get -1 = x.Find Potential Solutions: We have found two potential solutions for x: x = 9 from Case 1 and x = -1 from Case 2. However, we must check these solutions to ensure they satisfy the original equation.Check x = 9: Check x = 9 in the original equation |4x + 9| = 5x. Substitute x with 9 to get |4(9) + 9| = 5(9). Calculate the left side: |36 + 9| = |45| = 45. Calculate the right side: 5(9) = 45. Since both sides are equal, x = 9 is a solution.Check x = -1: Check x = -1 in the original equation |4x + 9| = 5x. Substitute x with -1 to get |4(-1) + 9| = 5(-1). Calculate the left side: |-4 + 9| = |5| = 5. Calculate the right side: 5(-1) = -5. Since both sides are not equal, x = -1 is not a solution.

Solve the equation for all values of $x$ . $\newline$ $|4 x+9|=5 x$ $\newline$ Answer: $x=$

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Solve the equation for all values of $x$ . $\newline$ $|4 x+9|=5 x$ $\newline$ Answer: $x=$