When it comes to resolving equations with absolute values, the process involves identifying solutions where the variable is encapsulated within an absolute value symbol. The central concept to remember is that the expression nestled within the absolute value can manifest as either a positive or a negative number. Therefore, the equation should be divided into two distinct scenarios for solving, taking into account both potential outcomes.
| Topic | Problem | Solution |
|---|---|---|
| None | QUESTION 3 - 1 POINT Find the solutions to the fo… | First, isolate the absolute value expression by subtracting 4 from both sides of the equation to ge… |
| None | $3|9-2 n|=-5 n$ | Split the equation into two possible scenarios: when the expression inside the absolute value is po… |
| None | Part B: Type your answer in the boxes below. Solv… | Split the absolute value equation into two separate equations, one for the positive case and one fo… |
| None | Question Watch Video Solve the equation for all v… | The given equation is \(|4x - 8| + 1 = 5x\). This is an absolute value equation, which means that t… |
| None | 5 For safety, the recommended height of a horse f… | The recommended height of a horse fence is 5 feet. However, due to uneven ground surfaces, the actu… |
| None | Solve each equation. 1. $|x|=8$ | The equation is \(|x|=8\). |
| None | Solve: $|4 x-6|<3$ Give your answer using interva… | Rewrite the absolute value inequality $|4x-6|<3$ as two separate inequalities: $-3<4x-6<3$. This is… |
| None | Solve the absolute value inequality. \[ |4(x-1)+1… | First, we remove the absolute value from the inequality |4(x-1)+10| ≤ 26. This gives us two inequal… |
| None | Solve the following equation. \[ |-2 x+3|+8=17 \]… | First, isolate the absolute value by subtracting 8 from both sides of the equation. This gives us \… |
| None | Solve the equation involving absolute value. (Ent… | The absolute value equation can be solved by considering two cases: when the expression inside the … |
| None | Solve the equation. \[ |4 x-5|=8 \] | The absolute value of a number is its distance from zero on the number line. Therefore, the equatio… |
| None | Solve and graph the solution: \[ |3 x+4| \geq 13 … | 1. \( 3x + 4 \geq 13 \) or \( 3x + 4 \leq -13 \) |
| None | \( 3|x-4|>9 \) | \(3|x-4|>9 \) |