Question

infinite algebra 1
multi-step inequalities
solve each inequality and graph its solution.

1. 3 < -5n + 2n

number line from -8 to 2 with ticks at -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2

Explanation:

Step1: Combine like terms

Simplify the right - hand side of the inequality \(3 < - 5n+2n\). Combining the terms with \(n\), we know that \(-5n + 2n=-3n\). So the inequality becomes \(3 < - 3n\).

Step2: Divide both sides by - 3

When we divide both sides of an inequality by a negative number, the direction of the inequality sign changes. Divide both sides of \(3 < - 3n\) by \(-3\). We get \(\frac{3}{-3}>\frac{-3n}{-3}\), which simplifies to \(- 1>n\) or \(n < - 1\).

Answer:

The solution to the inequality \(3 < - 5n + 2n\) is \(n < - 1\). To graph this solution, we draw an open circle at \(n=-1\) on the number line and shade the region to the left of \(-1\) (since \(n\) is less than \(-1\)).