Question

apply it
use what you learned to solve these problems.
7 the sum of 43.5 and a number, n, is no greater than 50.
what are all possible values of n? show your work.
solution
8 sebastián says that the graph below shows the solution set of the inequality
$2.5x \geq -20$. do you agree? explain.
9 solve the inequality $-48 < -8t$. then graph the solution set. show your work.

Explanation:

Problem 7

Step1: Translate to inequality

$43.5 + n \leq 50$

Step2: Isolate $n$ via subtraction

$n \leq 50 - 43.5$

Step3: Calculate the difference

$n \leq 6.5$

Step1: Solve the given inequality

$2.5x \geq -20$
$x \geq \frac{-20}{2.5}$
$x \geq -8$

Step2: Compare to the graph

The graph shows values less than or equal to -8 (arrow left, closed dot at -8), which is the opposite of the correct solution set.

Step1: Isolate $t$ via division

$-48 < -8t$
$\frac{-48}{-8} > t$
Note: Inequality flips when dividing by a negative number

Step2: Calculate the quotient

$6 > t$ or $t < 6$

Step3: Describe the graph

Draw a number line, place an open dot at 6, and draw an arrow pointing left to represent all values less than 6.

Answer:

All real numbers $n$ such that $n \leq 6.5$

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Problem 8