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Linear equations

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AI linear equation Solver

AI Linear Equation Solver solves linear equations with one unknown, brackets and fractions showing a clear step-by-step solutions

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About AI Linear Equation Solver

AI linear equation solver is powered by MathCrave AI algorithms to solve

  • Linear equation with arithmetic operations

  • Linear equations with one unknown

  • Linear equations involving brackets

  • Linear equation involving fractions

1. Distinguishing Between an Algebraic Expression and an Algebraic Equation:

  • An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It does not contain an equal sign (=). For example, 3x + 2y - 5 is an algebraic expression.

  • An algebraic equation, on the other hand, is a statement that two algebraic expressions are equal. It contains an equal sign (=) and can be solved to find the value(s) of the variables. For example, 2x + 3 = 7 is an algebraic equation.

2. Solving linear equations with one unknown:

A linear equation is an algebraic equation of degree 1, meaning the highest power of the variable is 1. To solve a linear equation, you isolate the variable on one side of the equation using inverse operations.

Example: Solve the equation 3x - 5 = 7

  • First, we add 5 to both sides to eliminate the -5:

  • 3x - 5 + 5 = 7 + 5

  • 3x = 12

  • Next, we divide both sides by 3 to isolate x:

  • (3x) / 3 = 12 / 3

  • x = 4

  • Therefore, the solution to the equation 3x - 5 = 7 is x = 4.

3. Linear equations involving brackets:

Linear equations can also involve brackets or parentheses to group terms.

Example: Solve the equation 2(3x + 5) = 18

  • First, we distribute the 2 to the terms inside the parentheses:

  • 2 3x + 2 * 5 = 18

  • 6x + 10 = 18

  • Next, we isolate the x-term by subtracting 10 from both sides:

  • 6x + 10 - 10 = 18 - 10

  • 6x = 8

  • Finally, we divide both sides by 6 to solve for x:

  • (6x) / 6 = 8 / 6

  • x = 4/3

  • Therefore, the solution to the equation 2(3x + 5) = 18 is

  • x = 4/3.

4. Linear equation involving fractions:

Linear equations can also involve fractions in the coefficients or variables.

Example: Solve the equation (1/2)x - 3/4 = 1/8

  • First, we isolate the x-term by adding 3/4 to both sides:

  • (1/2)x - 3/4 + 3/4 = 1/8 + 3/4

  • (1/2)x = 11/8

  • Next, we multiply both sides by the reciprocal of 1/2, which is 2/1, or simply 2:

  • (1/2)x * 2 = (11/8) * 2

  • x = 22/8

  • Simplify the fraction:

  • x = 11/4

  • Hence, the solution to the equation (1/2)x - 3/4 = 1/8 is

  • x = 11/4.

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