Linear Equation With One Variable
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The document discusses linear inequalities with one variable. It provides examples of inequalities such as 2x - 1 > 3 and 2x - 3 > 4x + 5. It then shows how to determine the solution set of each inequality by manipulating and solving the inequalities. Finally, it provides three practice problems for finding the solution set of additional inequalities.
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Here are the steps to solve each inequality and graph the solution:
1) m + 14 < 4
-14 -14
m < -10
Graph: m < -10
2) -7 > y-1
+1 +1
-6 > y
y < -6
Graph: y < -6
3) (-3)k < 10(-3)
-3
k > -30
Graph: k > -30
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-x -x
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-5 -5
x -4
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1. 油
Which of the following is the correct matrix representation of the October Inventory of small and large t-shirts and pants?
Inventory for August
Inventory for September
Inventory for October
Small
Large
Small
Large
Small
Large
T-Shirts
2
3
4
6
7
8
Pants
1
4
3
5
5
6
Answer
1. 油
If油油油find -2A.
Answer
1. 油
If油油油and 油油油find A - B.
Answer
1. 油
If油油油油 find 2A.
Answer
1. 油
Matrix A has dimensions 2 x 3. Matrix B has dimensions 3 x 6. These two matrices can be multiplied to find the product AB.
Answer油True油油False
1. 油
Evaluate 油油
Answer
Does not exist.
1. 油
Evaluate 油油
Answer
Does not exist
1. 油
Evaluate 油油
Answer
Does not exist.
1. 油
Find the determinant of 油油
Answer
14
-14
1
-1
1. 油
Find the determinant of 油油
Answer
-48
-56
56
48
1. 油
What is the determinant of the following matrix?
Answer
-10
-14
-20
-25
1. 油
What is the determinant of the following matrix? 油Does the matrix have an inverse?
Answer
5; no
5; yes
1; no
1; yes
1. 油
Is the following system consistent or inconsistent?
8x + y + 4 = 0
y = -8x - 4油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
7x + 6 = -2y
-14x -4y + 2 = 0油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
-2x - 2y = 6
10x + 10y = -30油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
2y = x - 7
-2x - 6y = -14油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
y = 2x + 5
-2x + y = -2油
Answer
consistent
inconsistent
If a system has exactly one solution it is called _______________.
Answer
consistent
inconsistent
independent
dependent
1. 油
Does the following system of equations have a solution?
油油
Answer
Yes
No
1. 油
What is the approximate solution of the following system of equations?
油油
Answer
(2, -7)
(-7, 2)
(7, 2)
(-7, -2)
1. 油
Solve the following system of equations by using the substitution method.
3y 2x = 11
y + 2x = 9
Answer
(2, 5)
(-2, -5)
(4, 5)
Inconsistent
1. 油
Solve the following system of equations by using the substitution method.
y = -3x + 5
5x 4y = -3
Answer
(-1, -2)
(2, 1)
(3, 4)
(1, 2)
1. 油
Solve the following system of equations by using the elimination method.
x y = 11
2x + y = 19
Answer
(1, 10)
(-1, -1)
(12, 2)
(10, -1)
1. 油
Solve the following system of equations by using the elimination method.油
-4x 2y = -12
4x + 8y = -24
Answer
(5, 3)
(-6, -6)
(3, 1)
(6, -6)
1. 油
Solve the following system of equations using matrices.
3x 2y = 31
3x + 2y = -1
Answer
(5, -8)
(3, 5)
(-3, 9)
(2, 8)
1. 油
Solve the following system of equations using matrices.
4x + 5y = -7
3x 6y = 24
Answer
(1, 4)
(2, -3)
(5, 6)
(3, 4)
1. 油
The sum of two numbers is 7. Four times the first number is one more than 5 times the second. Find the two numbe ...More Related Content
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2) Examples are provided to illustrate open sentences that can be made into closed sentences or equations by replacing variables with values. Exercises ask the reader to write open sentences as equations and solve simple equations.
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The document provides examples for solving systems of equations through various methods like elimination, substitution, and word problems. It demonstrates setting up systems as equations based on information provided, choosing an elimination method by adding or multiplying equations, isolating variables, substituting values, and checking solutions. Word problems are converted to systems of equations and then solved to find unknown variable values.Linear equation in one variable for class VIII by G R Ahmed
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This document summarizes key concepts from Chapter 3 of a math textbook, including:
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- Examples of solving linear equations by performing inverse operations like subtraction and division.
- Determining whether equations are linear based on the highest power of the variable, and providing examples of nonlinear equations.
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The document provides examples of solving linear and nonlinear inequalities algebraically and graphing their solution sets. For linear inequalities, the solutions are intervals of real numbers defined by the solutions to the corresponding equalities. For nonlinear inequalities, the solutions are unions of intervals where the factors of the corresponding equalities have the same sign. The document also demonstrates solving compound inequalities and inequalities involving rational expressions.1. 油Which of the following is the correct matrix representation .docx
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1. 油
Which of the following is the correct matrix representation of the October Inventory of small and large t-shirts and pants?
Inventory for August
Inventory for September
Inventory for October
Small
Large
Small
Large
Small
Large
T-Shirts
2
3
4
6
7
8
Pants
1
4
3
5
5
6
Answer
1. 油
If油油油find -2A.
Answer
1. 油
If油油油and 油油油find A - B.
Answer
1. 油
If油油油油 find 2A.
Answer
1. 油
Matrix A has dimensions 2 x 3. Matrix B has dimensions 3 x 6. These two matrices can be multiplied to find the product AB.
Answer油True油油False
1. 油
Evaluate 油油
Answer
Does not exist.
1. 油
Evaluate 油油
Answer
Does not exist
1. 油
Evaluate 油油
Answer
Does not exist.
1. 油
Find the determinant of 油油
Answer
14
-14
1
-1
1. 油
Find the determinant of 油油
Answer
-48
-56
56
48
1. 油
What is the determinant of the following matrix?
Answer
-10
-14
-20
-25
1. 油
What is the determinant of the following matrix? 油Does the matrix have an inverse?
Answer
5; no
5; yes
1; no
1; yes
1. 油
Is the following system consistent or inconsistent?
8x + y + 4 = 0
y = -8x - 4油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
7x + 6 = -2y
-14x -4y + 2 = 0油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
-2x - 2y = 6
10x + 10y = -30油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
2y = x - 7
-2x - 6y = -14油
Answer
consistent
inconsistent
1. 油
Is the following system consistent or inconsistent?
y = 2x + 5
-2x + y = -2油
Answer
consistent
inconsistent
If a system has exactly one solution it is called _______________.
Answer
consistent
inconsistent
independent
dependent
1. 油
Does the following system of equations have a solution?
油油
Answer
Yes
No
1. 油
What is the approximate solution of the following system of equations?
油油
Answer
(2, -7)
(-7, 2)
(7, 2)
(-7, -2)
1. 油
Solve the following system of equations by using the substitution method.
3y 2x = 11
y + 2x = 9
Answer
(2, 5)
(-2, -5)
(4, 5)
Inconsistent
1. 油
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y = -3x + 5
5x 4y = -3
Answer
(-1, -2)
(2, 1)
(3, 4)
(1, 2)
1. 油
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x y = 11
2x + y = 19
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(1, 10)
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(12, 2)
(10, -1)
1. 油
Solve the following system of equations by using the elimination method.油
-4x 2y = -12
4x + 8y = -24
Answer
(5, 3)
(-6, -6)
(3, 1)
(6, -6)
1. 油
Solve the following system of equations using matrices.
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3x + 2y = -1
Answer
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(3, 5)
(-3, 9)
(2, 8)
1. 油
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3x 6y = 24
Answer
(1, 4)
(2, -3)
(5, 6)
(3, 4)
1. 油
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- 1. BY Candida S.M (05) Fika Dahlia G.P . (11) Orryza Dwi J.A (19) Yeni Triastutik (29) Yunita Widyastuti (30) LIN EA R INEQUA LITY WITH ONE VARIABLE
- 2. The passing grade of the students is greater than or equal 60 It can be written as : n 60 LINEAR INEQUALITY WITH ONE VARIABLE
- 3. INEQUA LITY An open sentence using the sign <,>,,
- 4. THE EXAMPLE 2X - 1 > 3 X 8 > 15
- 5. Determine the set of solution of the inequality 2x - 1 > 3. If x is variable of { -1, 0, 2, 4, 5, 9, 11} 2x 1 > 3 2x 1 +1 > 3 + 1 2x + 0 > 3 + 1 2x > 4 2x > 4 2 2 x > 2 The solution set of 2x 3 > 4x + 5 is { 4, 5 , 9 ,11 }
- 6. Determine the set of solution of the inequality 2x 3 > 4x + 5 If x is variable of { -8 , -7 , -6 , , 6 } SOLUTION 2x 3 > 4x + 5 2x 3 +3 > 4x + 5 +3 2x > 4x + 8 2x 4x > 4x 4x +8 - 2x > 8 - 2x < 8 -2 -2 x < - 4 The solution set of 2x 3 > 4x + 5 is { -8 , -7 , -6 , -5 }
- 7. Practice Find the solution set of the following inequalities: 1. y + 2 > 6 , y { 1 , 3 , 5 , 7 , 9 } 2. 2x 3 < 7 , x is prime numbers 3. z + 4 > 4z 5 , z is whole numbers
- 8. THANK YOU