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Linear equation with arithmetic operations
Linear equations with one unknown
Linear equations involving brackets
Linear equation involving fractions
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.
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.
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.
Linear equations can also involve brackets or parentheses to group terms.
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.
Linear equations can also involve fractions in the coefficients or variables.
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.
