How do I solve a linear equation using equality properties?
You could demonstrate the process with an example by replacing the equal sign in the example with an inequality by using the less than or greater than sign (< or >) Then solve the inequality by your example. :)
To solve a linear equation using equality properties, follow these steps:
1. Start by simplifying both sides of the equation as much as possible by combining like terms and performing any necessary operations (such as addition, subtraction, multiplication, or division).
2. If there are any terms with variables on both sides of the equation, move all the terms to one side by using the commutative property (which allows you to change the order of terms) and the additive property (which allows you to add or subtract the same value on both sides).
3. Next, use the multiplicative property of equality to isolate the variable by dividing or multiplying both sides of the equation by a constant so that the coefficient of the variable becomes 1.
4. Continue simplifying the equation until you have isolated the variable on one side of the equation and obtained a specific value for it on the other side.
5. Check your solution by substituting the obtained value back into the original equation. If the equation holds true, then your solution is correct.
Let's illustrate this process with an example:
Example: Solve the equation 3x + 5 = 14
1. Start by simplifying both sides of the equation:
3x + 5 = 14
2. Move the constant term (5) to the other side of the equation:
3x = 14 - 5
3x = 9
3. To isolate the variable, divide both sides of the equation by the coefficient of x (3):
(3x)/3 = 9/3
x = 3
4. The variable x is now isolated, and its value is 3.
5. Check the solution by substituting x = 3 back into the original equation:
3(3) + 5 = 9 + 5 = 14
The equation remains true, so the solution x = 3 is correct.
By applying the equality properties correctly, you can solve linear equations step by step.