# Year Eight Mathematics Worksheets

Math can be a challenging subject for some kids, but with the right approach, it can also be a lot of fun! One of the concepts that students in middle school and high school need to understand is solving linear equations in one variable. In this article, we’ll be discussing two types of these equations: those with integral coefficients and those with rational coefficients.

Integral Coefficients: An integral coefficient is a whole number, such as 1, 2, 3, etc. When solving linear equations in one variable with integral coefficients, you need to isolate the variable on one side of the equation and then use inverse operations to find the value of the variable. Inverse operations are the opposite of the original operations in the equation. For example, if you add 3 to both sides of the equation, then you need to subtract 3 from both sides to find the value of the variable.

Here’s an example of a linear equation with an integral coefficient: 2x + 3 = 7 To find the value of x, we’ll need to isolate the variable on one side of the equation. We’ll start by subtracting 3 from both sides: 2x + 3 – 3 = 7 – 3 This gives us: 2x = 4 Next, we’ll divide both sides of the equation by 2: (2x) / 2 = 4 / 2 This gives us: x = 2 So the value of x in this equation is 2.

Rational Coefficients: A rational coefficient is a fraction, such as 1/2, 3/4, 5/6, etc. When solving linear equations in one variable with rational coefficients, you need to multiply both sides of the equation by the denominator of the fraction in order to clear the fraction. This means that the fraction will become a whole number and the equation will be easier to solve.

Here’s an example of a linear equation with a rational coefficient: (1/2)x + 3 = 7 To find the value of x, we’ll start by multiplying both sides of the equation by the denominator of the fraction, which is 2: (1/2)x + 3 = 7 2 * (1/2)x + 2 * 3 = 2 * 7 This gives us: x + 6 = 14 Next, we’ll subtract 6 from both sides of the equation: x + 6 – 6 = 14 – 6 This gives us: x = 8 So the value of x in this equation is 8.

In conclusion, understanding how to solve linear equations in one variable with integral and rational coefficients is an important step in developing your math skills. With practice and patience, you’ll find that this concept becomes easier to grasp and you’ll be able to solve equations with confidence. Remember, if you’re ever stuck or need help, don’t hesitate to reach out to your teacher or a tutor. They’re there to support you in your math journey!

# Year Eight Math Worksheet for Kids – Solving Linear Equations in One Variable Integral Coefficients and Rational Coefficients

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