Question

math 7
unit 2 homework 16 - introduction to inequalities
directions: show all work in order to receive full credit.

1. explain the difference between an equation and an inequality.
2. circle the numbers that satisfy ( n leq 2 )

1 -5 -2 0 ( \frac{3}{4} ) -1.5 2 3 -12
what is the greatest number in the solution set of ( n leq 2 )?

1. which of the following can not be a value for ( x ) if ( x geq -4 )?

a) -5 b) -4 c) 0 d) 3
what is the smallest number in the solution set of ( x geq -4 )?

1. graph ( x > 3 ) on a number line
2. write an inequality that represents the inequality below

Explanation:

1. Difference between equation and inequality

An equation shows equality ($=$), like $x + 2=5$. An inequality shows a relationship like $<$, $>$, $\leq$, or $\geq$, e.g., $x+2>5$.

2. Numbers satisfying $n\leq2$

• Check each number:
• $1\leq2$, $-5\leq2$, $-2\leq2$, $0\leq2$, $\frac{3}{4}\leq2$, $-1.5\leq2$, $2\leq2$, $3

leq2$, $-12\leq2$.

• The greatest number in the solution set of $n\leq2$ is $2$.

3. Value for $x\geq - 4$

• For $x\geq - 4$, $-5<-4$ (does not satisfy).
• The smallest number in the solution set of $x\geq - 4$ is $-4$.

4. Graphing $x > 3$

• On a number - line, draw an open circle at $3$ (since $x

eq3$) and shade to the right.

5. Writing the inequality from the graph

• The open circle is at $-1$ and the arrow points left. So the inequality is $x < - 1$.

Answer:

1. An equation uses $=$ to show equality; an inequality uses $<$, $>$, $\leq$, or $\geq$ to show a non - equal relationship.
2. Circled numbers: $1$, $-5$, $-2$, $0$, $\frac{3}{4}$, $-1.5$, $2$, $-12$; Greatest number: $2$.
3. A) $-5$; Smallest number: $-4$.
4. (Describe graph: open circle at $3$, shade right).
5. $x < - 1$.