Question

w4a1: unit 1 quiz
score: 45/100 answered: 11/24
question 12
solve and graph:
15x + 3 < 9x + 3 and - 3 + 5x ≤ 7x + 1
-5 -4 -3 -2 -1 0 1 2 3 4 5
clear all draw:

Explanation:

Step1: Solve the first inequality

Subtract \(9x\) and \(3\) from both sides of \(15x + 3<9x + 3\).
\(15x-9x+3 - 3<9x-9x + 3-3\), which simplifies to \(6x<0\), then \(x < 0\).

Step2: Solve the second inequality

Subtract \(5x\) and \(1\) from both sides of \(-3 + 5x\leq7x+1\).
\(-3-1+5x - 5x\leq7x-5x+1 - 1\), which simplifies to \(-4\leq2x\), then \(x\geq - 2\).

Step3: Find the intersection

The solution of the compound - inequality is the intersection of \(x < 0\) and \(x\geq - 2\), so \(-2\leq x<0\).

Step4: Graph the solution

On the number - line, put a closed circle at \(x = - 2\) (because \(x=-2\) is included in the solution, due to \(\geq\)) and an open circle at \(x = 0\) (because \(x = 0\) is not included in the solution, due to \(<\)), and shade the region between them.

Answer:

The solution is \(-2\leq x<0\). On the number - line, there is a closed circle at \(-2\), an open circle at \(0\), and the region between them is shaded.