Question

1. which of the following represents the solution for $5x - 3 leq 32$ 2. which of the following represents the solution for $7x - 2 < 54$

Explanation:

Step1: Solve the inequality \(5x - 3\leq32\)

Add \(3\) to both sides: \(5x-3 + 3\leq32 + 3\), so \(5x\leq35\).
Divide both sides by \(5\): \(x\leq7\).
On a number - line, a closed circle at \(7\) (since the inequality is \(\leq\)) and the line goes to the left.

Step2: Solve the inequality \(7x - 2\lt54\)

Add \(2\) to both sides: \(7x-2 + 2\lt54 + 2\), so \(7x\lt56\).
Divide both sides by \(7\): \(x\lt8\).
On a number - line, an open circle at \(8\) (since the inequality is \(\lt\)) and the line goes to the left.

Answer:

1. For \(5x - 3\leq32\), the solution is represented by option B (assuming option B has a closed circle at \(7\) and the line to the left).
2. For \(7x - 2\lt54\), the solution is represented by option C (assuming option C has an open circle at \(8\) and the line to the left).