Question

please help, fast‍♀️‍♀️

Answer 1

Inequalities are used to express unequal expressions.

The inequalities from the word problems are:

• $\mathbf{m - 3.5 \le -2}$.
• $\mathbf{0 \ge 2x + 1}$.
• $\mathbf{-\frac 12 \ge 2k - 4}$

The statements from the inequalities are:

• -4 is not a solution to $\mathbf{x + 8 < -3}$
• -6 is not a solution to $\mathbf{10 \le 3 - m}$
• -1 is not a solution to $\mathbf{-3x \le -12.5}$

• Graph b represents $\mathbf{x > -7}$

The word problems

1. A number minus 3.5 is less than or equal to -2

The statement can be broken down into the following expressions

$\mathbf{A\ number\ minus\ 3.5 \to m - 3.5}$

$\mathbf{less\ than\ or\ equal\ to\ -2 \to \le -2}$

So, when the expressions are brought together, we have:

$\mathbf{m - 3.5 \le -2}$

2. Zero is greater than or equal to twice a number x plus 1

The statement can be broken down into the following expressions

$\mathbf{Zero\ is\ greater\ than\ or\ equal\ to \to 0 \ge }$

$\mathbf{twice\ a\ number\ x\ plus\ 1\ \to 2x + 1}$

So, when the expressions are brought together, we have:

$\mathbf{0 \ge 2x + 1}$

3. -1/2 is at least twice a number k minus 4

The statement can be broken down into the following expressions

$\mathbf{-\frac 12\ is\ at\ least \to -\frac 12 \ge }$

$\mathbf{twice\ a\ number\ k\ minus\ 4\ \to 2k - 4}$

So, when the expressions are brought together, we have:

$\mathbf{-\frac12 \ge 2k - 4}$

None of the options is correct

The solutions

4. Tell whether -4 is a solution to x + 8 < -3

We have:

$\mathbf{x + 8 <-3}$

Subtract 8 from both sides

$\mathbf{x + 8 - 8 <-3 - 8}$

$\mathbf{x <-11}$

The above inequality means that:

x is less than -11

-4 is not a solution, because -4 is greater than -11

5. Tell whether -6 is a solution to 10 <= 3 - m

We have:

$\mathbf{10 \le 3 - m}$

Subtract 3 from both sides

$\mathbf{10 -3\le 3 - 3 - m}$

$\mathbf{7 \le - m}$

Multiply both sides by -1 (the inequality sign changes)

$\mathbf{-7 \ge m}$

Make m the subject

$\mathbf{m \le -7}$

The above inequality means that:

m is less than -7

-6 is not a solution, because -6 is greater than -7

6. Tell whether -1 is a solution to -3x <= -12.5

We have:

$\mathbf{-3x \le -12.5}$

Divide both sides by -3 (the inequality sign changes)

$\mathbf{x \ge 4\frac16}$

The above inequality means that:

x is greater than or equal to $\mathbf{4\frac16}$

-1 is not a solution, because -1 is less than $\mathbf{4\frac16}$

The graph

The inequality is given as: $\mathbf{x > -7}$

The less than sign (>) means that:

• The graph would use an open circle
• The arrow must point to the right

Only graph b satisfies this condition

Hence, the graph of $\mathbf{x > -7}$ is graph b

Read more about inequalities at:

https://brainly.com/question/15137133