Question

Solve each inequality. Is it graphed to open to the left, or closed to the right?

18. q + 0.5 > -2

20. 5x < 15

22. y/3 < (with the line under it) 2


24. 25.5 g > 102



Please show the work too.

Answer 1

What do you mean by " Is it graphed to open to the left, or closed to the right?"

Here is what I got for the inequalities;

\[q+0.5>-2\]
Subtract 0.5 from both sides.
\[q+0.5-0.5>-2-0.5\]
\[q>-2.5\]
Since it's a negative (-2.5) you flip the signs to make it a positive;
\[q<2.5\]


Next one;
\[5x<15\]
Divide both sides by 5;
\[5x \div5<15\div5\]
\[5x \div5=5\]
\[15\div5=3\]
So,
\[x<3\]


Next,
I assume this one is \[y \div3\le2\]
So, you reverse division with? Multiplication!
\[y \div3\times3\le2(3)\]
\[y \le6\]


Last one,
\[25.5g>102\]
Divide both sides by 25.5 to get g alone.
\[25.5g \div25.5>102\div25.5\]
\[102\div25.5=4\]
So,
\[g>4\]

Answer 2

Thank you! By open to the left or closed to the right, I meant if you were also graphing the answer to each problem.... would it be a closed circle with the line going all the way to the right or an open circle with the line going all the way to the left. Sorry it's weird to explain

Answer 3

Oh you mean on a number line?

Answer 4

Yessssss

Answer 5

Alright, give me a second to draw the number lines out for the inequalities. :p

Answer 6

Okay!

Answer 7

This is for the first one: