Solve: $| 4 x - 6 | < 3$
Give your answer using interval notation.

Answer

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Answer

The solution to the inequality $| 4 x - 6 | < 3$ is the interval $(\frac{3}{4}, \frac{9}{4})$ .

Steps

Step 1 ：Rewrite the absolute value inequality $| 4 x - 6 | < 3$ as two separate inequalities: $- 3 < 4 x - 6 < 3$ . This is because the absolute value of a number is less than 3 if and only if the number is between -3 and 3.

Step 2 ：Solve the inequalities to get $x = \frac{9}{4}$ and $x = \frac{3}{4}$ .

Step 3 ：The solution to the original inequality is the interval between these two values.

Step 4 ：The solution to the inequality $| 4 x - 6 | < 3$ is the interval $(\frac{3}{4}, \frac{9}{4})$ .

Solve: |4x−6|<3Give your answer using interval notation.

Answer

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Solve: $| 4 x - 6 | < 3$
Give your answer using interval notation.