Understanding Linear Equations in One Variable

Imagine you have a mystery number, and you want to find out what it is. That’s exactly what linear equations in one variable help us do! These equations have just one unknown value, called a variable, which we solve for using simple steps.

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What is a Linear Equation in One Variable?

A linear equation in one variable is an equation that has only one unknown and no exponents or complex terms. It follows the general form:

$$ ax + b = c $$

where $x$ is the unknown variable, and a, b, and c are numbers.

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Solving a Linear Equation

Let’s solve some examples step by step.

Example 1: Solve for $x$ in the equation:

$$2x + 5 = 15$$

Step 1: Subtract 5 from both sides:

$$2x + 5 - 5 = 15 - 5$$

$$2x = 10$$

Step 2: Divide by 2:

$$\frac{2x}{2} = \frac{10}{2}$$

$$x = 5$$

So, the mystery number is $5$!

Example 2: Solve for $x$ in the equation:

$$4x - 7 = 9$$

Step 1: Add 7 to both sides:

$$4x - 7 + 7 = 9 + 7$$

$$4x = 16$$

Step 2: Divide by 4:

$$\frac{4x}{4} = \frac{16}{4}$$

$$x = 4$$

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So the mystery number is 4!

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Why Are Linear Equations Important?

• Real-life applications: We use them to calculate expenses, distances, and even in cooking recipes!
• Foundation for algebra: Understanding linear equations helps in solving more complex math problems.

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Practice Question

Try solving this on your own:

$$3x - 4 = 11$$

Can you find the value of $x$? Keep practicing, and soon you’ll be a linear equations expert!