Questions: Consider the following linear inequality. 6z - 10.8 < -7.2 + 4z Step 1 of 2: Solve the inequality and express your answer in interval notation. Use decimal form for numerical values.

Solution Steps

To solve the inequality \(6z - 10.8 < -7.2 + 4z\), we need to isolate \(z\) on one side. First, subtract \(4z\) from both sides to simplify. Then, add \(10.8\) to both sides to further isolate the term with \(z\). Finally, divide by the coefficient of \(z\) to solve for \(z\). Express the solution in interval notation.

Start with the given inequality:

\[ 6z - 10.8 < -7.2 + 4z \]

Subtract \(4z\) from both sides to isolate terms involving \(z\):

\[ 6z - 4z - 10.8 < -7.2 \]

This simplifies to:

\[ 2z - 10.8 < -7.2 \]

Add \(10.8\) to both sides to isolate the term with \(z\):

\[ 2z < -7.2 + 10.8 \]

Simplify the right side:

\[ 2z < 3.6 \]

Divide both sides by 2 to solve for \(z\):

\[ z < \frac{3.6}{2} \]

Simplify the division:

\[ z < 1.8 \]

Final Answer