Solving equations with variables on both sides answer key – Unveiling the intricacies of solving equations with variables on both sides, this comprehensive guide empowers learners to navigate the complexities of algebraic equations with confidence. Embark on a journey of discovery, mastering the art of isolating variables, combining like terms, and simplifying equations to find the elusive solution.

Delving into the realm of algebra, we explore the fundamental concepts of equations with variables on both sides. Through a systematic approach, we unravel the steps involved in solving these equations, empowering individuals to tackle algebraic challenges with precision and efficiency.

Solving Equations with Variables on Both Sides: Solving Equations With Variables On Both Sides Answer Key

Solving equations with variables on both sides is a fundamental skill in algebra. It involves isolating the variable on one side of the equation to find its value.

The steps involved in solving such equations include:

1. Combining like terms on both sides of the equation.
2. Isolating the variable on one side of the equation.
3. Simplifying the equation by removing unnecessary terms or parentheses.
4. Checking the solution to ensure it is correct.

Isolating the Variable, Solving equations with variables on both sides answer key

To isolate the variable, perform the same operations on both sides of the equation until the variable is alone on one side.

For example, to solve the equation 3x + 5 = 2x + 10, we would:

• Subtract 2x from both sides: 3x – 2x + 5 = 2x – 2x + 10.
• Simplify: x + 5 = 10.
• Subtract 5 from both sides: x + 5 – 5 = 10 – 5.
• Simplify: x = 5.

Combining Like Terms

Combining like terms means adding or subtracting terms with the same variable and exponent.

For example, in the equation 2x + 3x – 5 = 10, we can combine the like terms 2x and 3x to get 5x.

Simplifying the Equation

Simplifying the equation involves removing unnecessary terms or parentheses.

For example, in the equation (x + 2) + 5 = 10, we can remove the parentheses to get x + 7 = 10.

Checking the Solution

To check the solution, substitute the value of the variable back into the original equation.

For example, to check if x = 5 is a solution to the equation 3x + 5 = 2x + 10, we would substitute x = 5 into the equation and see if it holds true.

3(5) + 5 = 2(5) + 10

15 + 5 = 10 + 10

20 = 20

Since the equation holds true, we can conclude that x = 5 is the correct solution.

Examples and Practice

Difficulty Level	Equation
Easy	2x + 5 = 15
Medium	3x 5 = 2x + 10
Hard	(x + 2)(x 3) = x^2 5

Question & Answer Hub

What is the first step in solving an equation with variables on both sides?

The first step is to isolate one of the variables on one side of the equation.

How do you combine like terms when solving equations?

To combine like terms, add or subtract the coefficients of the terms with the same variable.

Why is it important to check the solution to an equation?

Checking the solution ensures that the solution is correct and satisfies the original equation.