Solve the following equation for x.
4|5x - 2| - 1 = 3

Question

Quizplus · Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. 4|5x - 2| - 1 = 3 In this equation, we see the use of the absolute value symbol, | |. The absolute value of a number is the magnitude of that number. In other words, it is the number of places it is from zero. This means that the absolute value of a negative number is simply the number of spaces it is away from zero (in either direction). For example, |- 3| = 3 because -3 is three places from zero. When there is an absolute value within an equation, it represents the absolute value of that number, when x is known. When we see the absolute value symbol, it alerts us that the value of the number inside can be either positive or negative. Therefore, we must solve for both possibilities, and separate the problem into the positive answer and the negative answer and solve for both: First, however, we can simplify the equation. Add 1 to both sides of the equation in order to eliminate the (-1) from the left side of the equation. 4|5x - 2| - 1 + 1 = 3 + 1 4|5x - 2| = 4 Divide both sides of the equation by 4, since it is the coefficient (the number that is multiplying) of the absolute value. 4|5x - 2| ÷ 4 = 4 ÷ 4 |5x - 2| = 1 Now, we can solve for the positive and negative answers. 11ec0fb7_2744_4594_95f0_8bc4c32c74fc_NR0002_00 Answer: x can be equal to both ³⁄₅and ¹⁄₅_.

Solve the Following Equation for X