91Ó°ÊÓ

Linear equations are mathematical sentences that show the equality between two expressions. They have a standard form of ax + b = c, where:

• 'a' and 'b' are constants (numbers)
• 'x' is the variable
• '=' is the equality sign
• 'c' is another constant

In the given exercise, the equation is 0.4x + 0.6 = 0.5x - 1.2.

This is a linear equation because it has:

• One variable, 'x', that is not raised to any power (which means it is just 'x')
• Decimal coefficients, like 0.4 and 0.5.
• Constant terms, like 0.6 and -1.2.

Solving it involves isolating the variable on one side of the equation and simplifying step by step.

Decimal coefficients are simply numbers with decimal points that are multiplied by the variable in an equation.
Unlike whole number coefficients, decimal coefficients can sometimes make the calculations seem more complicated.

Here's what you need to keep in mind:

• A coefficient is just a number that multiplies the variable. In the equation 0.4x + 0.6 = 0.5x - 1.2, 0.4 and 0.5 are the coefficients of 'x'.
• Decimals are just parts of wholes; you can treat them like any other number when performing arithmetic >operations like addition, subtraction, multiplication, and division.

In our exercise, we first move all 'x' terms to one side:
0.4x + 0.6 - 0.4x = 0.5x - 1.2 - 0.4x
This simplifies to:
0.6 = 0.1x - 1.2.

The coefficient for 'x' on the right side now is 0.1. We handle it just like a whole number when isolating 'x'.

Solving for variables means finding the value of the unknowns in the equation that makes the equation true.

For our specific problem, we need to find the value of 'x' that satisfies 0.4x + 0.6 = 0.5x - 1.2.

Step 1 is to isolate 'x' on one side of the equation. We first subtract 0.4x from both sides:
0.4x + 0.6 - 0.4x = 0.5x - 1.2 - 0.4x,
which simplifies to 0.6 = 0.1x - 1.2.

Step 2 is to move the constants to the other side.
We add 1.2 to both sides: 0.6 + 1.2 = 0.1x - 1.2 + 1.2,
which simplifies to 1.8 = 0.1x.

Step 3 is to solve for 'x' by dividing both sides by 0.1: \( x = \frac{1.8}{0.1} \),
which simplifies to x = 18.

Now we have successfully found the value of 'x' that makes the original equation true!