Solve each inequality.

1. |2x - 3| /leq 11

1 answer

To solve the inequality \(\left| 2x - 3 \right| \leq 11\), we can break it down into two separate inequalities:

  1. \(2x - 3 \leq 11\)
  2. \(2x - 3 \geq -11\)

Let's solve each inequality step by step.

1. Solve \(2x - 3 \leq 11\)

Add 3 to both sides:

\[ 2x \leq 11 + 3 \] \[ 2x \leq 14 \]

Now, divide both sides by 2:

\[ x \leq 7 \]

2. Solve \(2x - 3 \geq -11\)

Add 3 to both sides:

\[ 2x \geq -11 + 3 \] \[ 2x \geq -8 \]

Now, divide both sides by 2:

\[ x \geq -4 \]

Combining the Results

Now we combine the results from both inequalities:

\[ -4 \leq x \leq 7 \]

In interval notation, the solution is:

\[ [-4, 7] \]