Evaluate the expression 81p² + 16q² - 72pq when P =  and q =

Write a compound inequality for each graph:

Solve the compound inequality: -12 ≤ 7x + 9 < 16 and graph the solution

Observe the diagram carefully and find x and y.

Observe the given window and explain which lines are parallel.

Find the value of x.

Ajit is 21 years younger than his father. What is their total age in 7 years' time?

Solve each compound inequality and graph the solution.
2x+5 > -3 and 4x+7 < 15

When two inequality statements are joined by the words "or" or "and," the sentence is said to be compound inequality. The preposition "and" denotes that both statements in the compound sentence are true simultaneously. It is where the solution sets for the several statements to cross or overlap. The conjunction "or" indicates that the whole compound statement is true.
Example
Solve for x: 3 x + 2 < 14 and 2 x – 5 > –11
Here we have to solve each inequality individually. Because the joining word is "and," the overlap or intersection is the desired outcome.
3x+2<14 and 2x-5>-11
3x<12 2x>-6
x<4 x>-3
Numbers to the left of 4 are represented by x < 4, and the right of -3 is represented by x > -3. The solution set consists of {x| x > –3 and x < 4}

Solve the compound inequality -3x + 2 > -7 or 2(x - 2) ≥ 6. Graph the solution:

The combination of two inequalities using "and" or "or" results in a compound inequality. Each inequality in a compound inequality can be solved using the same steps as a normal inequality, but when combining the solutions, it makes a difference whether "and" or "or" is used to join the two inequality solutions together.
¶For instance, 1 < x < 3 is equivalent to "x > 1 andx < 3". The use of "or" is always used to specifically refer to a compound inequality, on the other hand.
¶x > 1: Since there is no "=" at 1, we receive an open dot. Additionally, since 1 has ">," we draw an arrow to the right of it.

What would be sufficient information to prove that c || d?

Find the measure of angle x.

Solve the compound inequality 5x+7 < 13 or -4x+3 > 11. Graph the solution.

A Compound inequality is a connection between two inequality statements by the words "or" or "and." The conjunction "and" denotes the simultaneous truth of both statements in a compound sentence. It is the point where the solution sets for the various statements cross over or intersect. The conjunction "or" denotes that the entire compound sentence is true as long as either of the two statements is true — the union or combination of the solution sets for each particular statement.
Let's see x: 2 x + 7 < –11 or –3 x – 2 < 13. Solve each inequality on its own. Combine the solutions, i.e., determine the union of the solution sets for each inequality phrase since the connecting word is "or." Both x < –9 and x > -5 denote all the numbers on the left of those two particular values. Written as follows is the solution set:
{ x| x < -9 or x > -5}

If 3x- 7y = 10 and x y = - 1, find the value of 9x² + 49y²

Which line segment will give the distance between the parallel shelves of the given table?

Is c parallel to d? Justify your answer

Write a compound inequality for each graph :