Post your responses to the following. Answer each question in a separate paragraph:


Techniques that can simplify solving equations and inequalities are to clear fractions and decimals when solving linear equations and inequalities.

1. Demonstrate how fractions are cleared with an example with detailed algebraic calculations.
2. Demonstrate how decimals are cleared with an example with detailed algebraic calculations.


Write an equation or inequality that uses either decimal or fractional coefficients respectively for the variables for your classmates to solve.

1.

e.g. (2/3)x -4 = x/2 +1
multiply each term by 6, the LCD

4x - 24 = 3x + 6
x = 30

e.g.
.05x + ,2x = 5
multiply by 100, (since my longest decimal string is 2)
5x + 20x = 500
etc

1. To clear fractions in an equation, we can multiply both sides of the equation by the least common denominator (LCD) of all the fractions involved. Let's consider the following example:

Solve the equation: 3/4x + 1/2 = 5/6

To clear the fractions, we first find the LCD, which in this case is 12. We then multiply both sides of the equation by 12:

12 * (3/4x + 1/2) = 12 * (5/6)

This simplifies to:

9x + 6 = 10

Now, we can proceed to isolate the variable on one side of the equation by subtracting 6 from both sides:

9x = 10 - 6

9x = 4

Finally, we divide both sides of the equation by 9 to solve for x:

x = 4/9

2. To clear decimals in an equation, we can multiply both sides of the equation by a power of 10 that will eliminate the decimals. Let's consider the following example:

Solve the equation: 0.3x - 0.2 = 0.4

To clear the decimals, we can multiply both sides of the equation by 10 to get rid of the decimal point:

10 * (0.3x - 0.2) = 10 * 0.4

This simplifies to:

3x - 2 = 4

Next, we can isolate the variable by adding 2 to both sides of the equation:

3x = 4 + 2

3x = 6

Finally, divide both sides of the equation by 3 to solve for x:

x = 6/3

As for the equation or inequality that uses either decimal or fractional coefficients, let's create an inequality:

Example: 1/2x + 0.75 ≥ 1.5

This inequality involves the variable x and uses fractional coefficients (1/2 in this case) and a decimal coefficient (0.75). To solve this inequality, you would apply the same techniques mentioned earlier (clearing fractions and decimals) to isolate the variable on one side of the inequality symbol.