Questions: Solve for (z). [ 18<84-z ]

Solve for (z). [ 18<84-z ]
Transcript text: Solve for $z$. \[ 18<84-z \]
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Solution

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Solution Steps

To solve the inequality \(18 < 84 - z\), we need to isolate the variable \(z\). This involves two main steps:

  1. Subtract 84 from both sides of the inequality.
  2. Multiply both sides by -1 and reverse the inequality sign.
Step 1: Isolate the variable term

We start with the given inequality: \[ 18 < 84 - z \]

To isolate the term involving \( z \), we subtract 84 from both sides of the inequality: \[ 18 - 84 < -z \]

Step 2: Simplify the inequality

Next, we simplify the left-hand side: \[ -66 < -z \]

Step 3: Solve for \( z \)

To solve for \( z \), we need to get rid of the negative sign in front of \( z \). We do this by multiplying both sides of the inequality by -1. Remember, when we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign: \[ 66 > z \]

This can also be written as: \[ z < 66 \]

Final Answer

\[ \boxed{z < 66} \]

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