Question

indiana algebra 1
date
multi - step inequalities
solve each inequality and graph its solution:

1. $3 < -5n + 2n$

1. $8x + 2 + 6x > 14$

1. $-g - 4g > -10$

1. $18 \geq 5k + 4k$

1. $9 \geq -2m + 2 < 1$

1. $-3 - 6(4x + 6) > -111$

1. $6 - 4(6n + 7) \geq 132$

1. $-138 \geq -6(6b - 7)$

1. $167 < 6 + 7(2 - 7r)$

1. $5(6 + 3r) + 7 \geq 127$

1. $-8x + 2x - 16 < -5x + 7x$

1. $-1 - 6x - 6 > -11 - 7x$

Explanation:

Step1: Solve the inequality \( 3 < -5n + 2n \)

First, combine like terms on the right side: \( -5n + 2n = -3n \). So the inequality becomes \( 3 < -3n \).

Step2: Isolate \( n \)

Divide both sides by \(-3\). Remember, when dividing by a negative number, the inequality sign flips. So we get \( \frac{3}{-3} > n \), which simplifies to \( -1 > n \) or \( n < -1 \).

Step3: Graph the solution

On a number line, we draw an open circle at \(-1\) (since \( n \) is not equal to \(-1\)) and shade to the left of \(-1\) to represent all numbers less than \(-1\).

Answer:

The solution to the inequality \( 3 < -5n + 2n \) is \( n < -1 \), and the graph has an open circle at \(-1\) with shading to the left.