Solve the equation.
$| 4 x - 5 | = 8$

Answer

Expert–verified

Hide Steps

Answer

The solutions to the equation are $\frac{13}{4}$ and $- \frac{3}{4}$ .

Steps

Step 1 ：The absolute value of a number is its distance from zero on the number line. Therefore, the equation $| 4 x - 5 | = 8$ means that $4 x - 5$ is either 8 units away from zero to the right (positive direction) or 8 units away from zero to the left (negative direction). This gives us two equations to solve: $4 x - 5 = 8$ and $4 x - 5 = - 8$ .

Step 2 ：Solving the first equation $4 x - 5 = 8$ , we get the solution $x = \frac{13}{4}$ .

Step 3 ：Solving the second equation $4 x - 5 = - 8$ , we get the solution $x = - \frac{3}{4}$ .

Step 4 ：The solutions to the equation are $\frac{13}{4}$ and $- \frac{3}{4}$ .

Solve the equation.|4x−5|=8

Answer

Popular Problems

Solve the equation.
$| 4 x - 5 | = 8$