Solving inequalities is similar to solving a regular equation. The only thing you need to worry about with inequalities is that when you are dividing or multiplying by a negative number, you must flip the inequality sign. You won't have to worry about that here if the coefficient in front of x is positive when you divide!
Also remember:- To add/subtract fractions, you have to turn all mixed numbers into improper fractions (if needed), <span>find a common denominator on both fractions (if needed), add/subtract the numerators, put the sum/difference over the common denominator, and
simplify if needed.
- To multiply fractions, multiply the numerators and multiply the denominators. Put the product of the numerators over the product of the denominators.
- To divide fractions, remember that dividing by a fraction is the same as multiplying by the inverse of that fraction (aka fraction flipped).
- To turn mixed numbers into improper fractions, multiply the whole number by the denominator of the fraction. Add the numerator of the fraction to the product you get, and put that final sum over the original denominator.
Back to the problem:
</span>You are told that

and you have to solve for x.
<span>
1) </span>Using the info for converting mixed numbers to improper fractions from above, you know that

and

and

. Now add/subtract using the info above, isolating the variable x by adding

to both sides and subtracting

from both sides.

2) Divide both sides by

to get the inequality for x. Remember the info for dividing from above:
Your final answer is x <
or x <
.
Hello!
Find the coordinate where x = -1:
At x = -1, y = 1, so the coordinate is (-1, 1).
Find the coordinate where x = 2:
At x = 2, y = -2, so the coordinate is (2, -2).
Find the rate of change between the points using the slope formula:

Plug in the coordinates above:

Simplify:
Thus, the rate of change between the points is -1.
Answer:
x + 4y ≤ 15; y ≥ 0
Step-by-step explanation:
The graph doesn't do a very good job of modeling any of the given equations. However, the equations listed above seem the best fit.
The slope of the top (left) line is negative, so the equation will be of the form ...
x + 4y = something
When y=0, x=15, so the "something" is expected to be 15.
However, the line appears to go through points (6, 2) and (-2, 4). Both of these points are on the line x + 4y = 14.
The graph is shaded <em>below the line</em> so the values of x and y that are in the shaded area will add to <em>less than</em> 15 (or 14). Hence, the inequality will be ...
x + 4y ≤ something . . . . . part of the 3rd answer choice
The fact that the shading does not go below y=0 means the other limit is ...
y ≥ 0 . . . . . part of every answer choice.
Not enough information
Explanation: in order for them to be congruent it must have at least two equal sides or 2 equal angles