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

Answer

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Answer

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

Steps

Step 1 ：Rewrite the absolute value inequality $|4x-6|<3$ as two separate inequalities: $-3<4x-6<3$. 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 $|4x-6|<3$ is the interval $\boxed{(\frac{3}{4}, \frac{9}{4})}$.

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

Answer

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