1. Solve for \( x \) and illustrate the answer on a number line \[ 1-2 x>x-2 \]

To solve the inequality \( 1 - 2x > x - 2 \), first, we rearrange it by moving all terms involving \( x \) to one side and constant terms to the other. 1. Add \( 2x \) to both sides: \[ 1 > 3x - 2 \] 2. Then add \( 2 \) to both sides: \[ 3 > 3x \] 3. Now divide both sides by \( 3 \): \[ 1 > x \quad \text{or} \quad x < 1 \] So, \( x < 1 \) is our solution. To illustrate this on a number line, draw a line and put an open circle at \( 1 \) to indicate that \( 1 \) is not included in the solution. Then shade all the area to the left of \( 1 \) to show that all values less than \( 1 \) are included in the solution set. Now you've got it! A fun fact is that inequalities can often look intimidating, but they often just require similar steps as regular equations. Just remember to reverse the inequality sign when multiplying or dividing by a negative number!