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Equation

Equation. --- An equation is a mathematical statement that asserts the equality of two expressions . An equation involves an unknown , typically written x.   Here is a simple example: x + 64 = 100. We say that an equation has two sides: the left side, x + 64, and the right side, 100.

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Equation

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  1. Equation --- An equation is a mathematicalstatement that asserts the equality of two expressions. An equation involves an unknown, typically written x.   Here is a simple example: x + 64 = 100. We say that an equation has two sides: the left side, x + 64, and the right side, 100. HessahWaelHiji Al-Shemmary

  2. Inequalities --- An inequality is a mathematical sentence including one of the inequality signs ( < , > , ≤ or ≥ ) between two sides. As an example a linear inequality has this standard form: ax + b < c. --- The solution set is the set of elements of real numbers which satisfy the given equation or the inequality HessahWaelHiji Al-Shemmary

  3. Exercises: (1) Solve the following equations (a) 2x + 3 = 5 (b) 3x – 4 = 7 (c) x + 5 = 3x – 6 (d) 4(x - 2) = 3(x - 5) (e) (3x - 5) + 4 = x - 11. (2) Find the solution of the following inequalities: (a) 2x – 4 < 6 (b) 3 x - 5≥ 10 (c) 3x ≤ 4x +1 (3) Determine whether each of the following represents an equation or an inequality or neither: (a) x + 5 (b) 9 - 5 = 4 (c) x + 7 = 12 (d) 2x – 4 < 6 (e) x – 17 (f) x – 2y = 5 (4) Study the possibility of solving each of the following equations in or : (a) 3x = 8. (b) 3x + 12 = 6. (c) 2x - 15 = 8. (5) If 4 is added to a number, then the result is 14. What is this number? (6) The sum of three consecutive natural numbers is 27. Find these numbers. (7) Find the solution set of the inequality -1 ≤ 2x + 3 < 13 in , then represent it on the number line HessahWaelHiji Al-Shemmary

  4. Matrixes In mathematics, a matrix is a rectangular array of numbers, such as 1, 3, 6, -1are called the entries. Entries are often denoted by a variable with two subscripts, as shown on the right; thus in the example above, a2,1 = 6. Matrices of the same size can be added and subtracted entrywise and matrices of compatible sizes can be multiplied. These operations have many of the properties of ordinary arithmetic, except that matrix multiplication is not commutative, that is, AB and BA are not equal in general. Matrices are a key tool in linear algebra. Matrices can also keep track of the coefficients in a system of linear equations HessahWaelHiji Al-Shemmary

  5. Exercises: For A = and B = (1) Add and subtract the two matrices (2) Multiply A by B (AB) and B by A (BA). HessahWaelHiji Al-Shemmary

  6. Systems of linear equations --- Now consider the following two-variable system of linear equations: y = 3x – 2y = –x – 6 We can deal with them together at the same time. In particular, we can graph them together on the same axis system, like this: A solution for a system of equations is any point that lies on each line in the system  HessahWaelHiji Al-Shemmary

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  9. Exercises:  (1) Determine whether either of the points (–1, –5) and (0, –2) is a solution to the given system of equations. y = 3x – 2y = –x – 6 (2) Find the solution of the system of linear equations – 3x + y= – 2x + y = 6 --- We can convert a system of linear equations into a matrix equation like this: – 3x + y= – 2x + y = 6 HessahWaelHiji Al-Shemmary

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