Question

w4a1: unit 1 quiz
score: 40/100 answered: 10/24
question 11
solve and graph:
13x + 1 > 8x + 16 or 3 + 2x ≥ 5x + 3
-5 -4 -3 -2 -1 0 1 2 3 4 5
clear all draw:

Explanation:

Step1: Solve the first inequality

Subtract \(8x\) from both sides of \(13x + 1>8x + 16\):
\(13x-8x+1>8x - 8x+16\), which simplifies to \(5x+1>16\). Then subtract 1 from both sides: \(5x+1 - 1>16 - 1\), getting \(5x>15\). Divide both sides by 5: \(x > 3\).

Step2: Solve the second inequality

Subtract \(2x\) from both sides of \(3 + 2x\geq5x+3\):
\(3+2x-2x\geq5x - 2x+3\), which simplifies to \(3\geq3x + 3\). Then subtract 3 from both sides: \(3-3\geq3x+3 - 3\), getting \(0\geq3x\). Divide both sides by 3: \(x\leq0\).

Step3: Graph the solutions

For \(x > 3\), we use an open - circle at \(x = 3\) and draw an arrow to the right. For \(x\leq0\), we use a closed - circle at \(x = 0\) and draw an arrow to the left.

Answer:

The solution of the compound inequality is \(x\leq0\) or \(x>3\). On the number - line, we have a closed circle at \(x = 0\) with an arrow to the left and an open circle at \(x = 3\) with an arrow to the right.