Question

ann will buy at least 6 meters of fabric. the fabric costs 2 dollars per meter. lets look at the possible numbers of dollars ann will spend on fabric.
(a) fill in the blanks to write an inequality that can be used to find x, the number of dollars ann will spend on fabric. choose only from (2 + x), (2 - x), (x - 2), (2x), (\frac{2}{x}), (\frac{x}{2}), (<), (leq), (>), (geq), or 6.
inequality:
(b) find the possible numbers of dollars ann will spend on fabric. write your answer as an inequality solved for x.
(c) on the number line below, graph the solution that represents the possible numbers of dollars ann will spend on fabric.

Explanation:

Step1: Define variables and relationship

Let $x$ = total cost (dollars), $m$ = meters of fabric. Since cost = $2 \times m$, $m = \frac{x}{2}$.

Step2: Set up initial inequality

Ann buys at least 6 meters, so $m \geq 6$. Substitute $m = \frac{x}{2}$:
$\frac{x}{2} \geq 6$

Step3: Solve for x

Multiply both sides by 2:
$x \geq 12$

Step4: Graph the solution

On a number line, plot a closed dot at 12 (since 12 is included) and draw an arrow to the right (all values greater than or equal to 12).

Answer:

(a) $\frac{x}{2} \geq 6$
(b) $x \geq 12$
(c) A closed dot at 12 on the number line, with an arrow extending to the right towards larger numbers.