Consider the set of real numbers: { x | x < −3 or x > 4 }. Graph the set of numbers on the real number line.   Write the set of numbers using interval notation

Q: The perimeter of a rectangle is 40 feet. Describe the possible lengths of a side if the area of the…

A: Perimeter of the rectangle is 40 feet We know that the perimeter formula is 2(length + width) Let…

Q: Solve the absolute value and find the intervals 7-4X <4

A: | 7 - 4x | &lt;= 4

Q: Rewrite the expression using the given property of real numbers. Commutative property of Addition, x…

A: Given, Rewrite the expression using the given property of real numbers. Commutative property of…

Q: For what values of x is the expression   3x − x2 defined as a real number? (Enter your answer using…

A: Real numbers are the numbers that can be represented on the real number line. It can be positive,…

Q: Graph the inequality on a number line and represent it in interval notation. - 8 <x<4 Choose the…

A:

Q: Use intervals to determine the values of x that satisfy the following inequality: 3x³-25x²-52x + 20>…

A: The given inequality is: 3x3-25x2-52x+20&gt;0 Find the zero of the polynomial px=3x3-25x2-52x+20.…

Q: Choose any points a and b on a number line. Find the values of a-b and b-a. What do the absolute…

A: Let  a=0  and  b=1

Q: Solve the absolute value and find the intervals |7 – 4 X | < 1

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Q: Fill in the blank so that the resulting statement is true. In interval notation, (-2,00) represents…

A: Given interval is: (-2,∞)which means -2 is not included in the interval.

Q: Solve ((use interval notation to express solution sets and graph each solution set on a number…

A:

Q: Write the expression  |x − 5| + |x − 7|  without the absolute value symbols if x is in the given…

A: Consider the given expression as According to definition of absolute value of function,

Q: Solve the absolute value and find the * intervals |7 – 4 X |< 1

A: |x| = +x, -x

Q: Express the distance between the given numbers using absolute value. Then find the distance by…

A: Distance between -6 and 8 is |8-(-6)|.

Q: Use absolute value notation to define the interval (or pair of intervals) on the real number line.…

A: Consider the figure given below :

Q: State all integer values of x in the interval [-5, 2] that satisfy the following inequality: 3x + 3…

A: This question is based on inequality.

Q: Graph the set {x |x<-5} on the number line. Then, write the set using interval notation. {x]x s -5}…

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Q: Solve each indentity. Graph the solution on a number line and express it in interval notation. a.…

A: Given  The inequality is 43x+7≥26x+14.

Q: Plot each number on the real number line, or explain why the number is not on the real number line.…

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Q: (a) Graph the intervals (-5, 3] and (2, 0) on the real number line.

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Q: Graph the inequality on a number line and represent it in interval notation. -7<x<1 Choose the…

A: given inequality   -7&lt;x&lt;1

Q: Graph the intersection of x ≥ -2 and x < 1, and give the solutions in interval notation

A: The given inequality is x≥-2 and x&lt;1.

Q: State all integer values of x in the interval -4, 2 that satisfy the following inequality: 4x + 5 <…

A: Given the inequality  4x + 5 &lt; -6 We need to find the values of x which satisfies the given…

Q: Express the distance between the given numbers using absolute value. Then find the distance by…

A:

Q: 11. Find all the real values that satisfy 27 +343 63 +147 || - 37 21

A: The given equation,     27x+343x63x+147x=3721

Q: (a) On the real number line, graph all numbers x for which x &gt; 4.(b) On the real number line,…

A: (1) we have to graph all numbers x for which x &gt; 4. The shaded region represents the shaded…

Q: Graph the solution set of the inequality on a number line and then write it in interval notation.…

A:

Q: Express the distance between the given numbers using absolute value. Then find the distance by…

A: Distance between 2 and 17: 2-17=-15=15

Q: Find all real number values for x which would make the inequality true: (x – 3)(x + 5) <9

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Q: Solve the absolute value and find the * intervals |7 – 4 X|<1

A: See the attachment

Q: Solve the inequality for real x:  37 – (3x + 5) &gt; 9x – 8 (x – 3)

A: Given:

Q: The domain for all variables in the expressions below is the set of real numbers.Determine whether…

A: The statement (i) is true. The proof of that has been given in step 2.

Q: Express the solution set in interval notation and graph the set on a number line. The solution set…

A: Given, the solution set consists of all real numbers greater than -4. Let,x represent the solution…

Q: Solve the absolute value and find the intervals |7 – 4 X|< 1

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Q: Given the sets of real numbers defined by the intervals, find the union or intersection as…

A: U: Union is the addition of both sets and combining it into one set. Example : 1,2∪3,4=1,2,3,4

Q: What is the absolute value of a number a and what is it denoted by?

A: Absolute value:   The absolute value of a real number “a” is denoted by |a| (mod a) and it is the…

Q: Express the solution set in interval notation and graph the set on a number line. The solution set…

A: Given: solution sets consists of real numbers &lt; -3To graph this in the interval notation

Q: Write the solution set in interval notation. 4x < 28 The solution set is x<7 (Type your answer in…

A: Given 4x&lt;28

Q: Describe all the x-values at a distance of 19 or less from the number 9. Enter your answer in…

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Q: Rewrite the expressions without using the absolute value symbol. |x − 7|  if  x < 7

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: -2x > - 12 if all real numbers satisfy the inequality, select all real numbers. If no real numbers…

A: solution:--2x&gt;-122x&lt;12    {inequality changed when both sides are multiplied by…

Q: Solve the inequality and give the solution in interval notation. -3st+4<5 The answer in interval…

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Q: B and C are sets of real numbers defined as follows. B = {y |y 6} Write BU Cand B N C using interval…

A: B and C are sets of real numbers defined as follows.…

Q: Rewrite the expression without using the absolute value symbol. |x + 1|   if x ≥ −1     if x < −1

A: The given absolute value x+1 we have to rewrite the expression without using absolute symbol.

Q: Solve the inequality. Express the answer using interval notation. |5x – 8| < 10

A: The objective is to solve the inequality and express the answer using interval notation.

Q: Solve the inequality and graph the solution set. Write the solution set in (a) set-builder notation…

A: Consider the given inequality -34z-4&gt;-1. Solve the given inequality for z as follows.…

Q: The domain for all variables in the expressions below is the set of real numbers. Determine whether…

A:

Q: The domain for all variables in the expressions below is the set of real numbers. Determine whether…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.