Multi-Step Equations Worksheet: Variables on the Same Side

This worksheet provides practice in solving multi-step equations with variables on one side. It contains 10 problems that require students to demonstrate their understanding of algebraic concepts and problem-solving skills.

Highlight: Students are instructed to show all their work, which is crucial for developing proper mathematical reasoning and communication skills.

The problems range from simpler equations like 3$x - 2$ = 24 to more complex ones such as $3x + 6$ - 4x = 12. Each solution is presented step-by-step, illustrating the process of solving multi-step equations.

Example: Problem 1 solution: 3$x - 2$ = 24 3x - 6 = 24 +6 +6 3x = 30 x = 10

This example demonstrates the process of distributing the 3, combining like terms, and then isolating the variable to solve for x.

Vocabulary: Multi-step equations - Equations that require more than one step to solve, often involving operations such as distribution, combining like terms, and isolating variables.

The worksheet covers various types of equations, including those with:

• Parentheses that need to be distributed
• Multiple instances of the variable on one side
• Fractions and negative numbers

Definition: Distributing - The process of multiplying a factor by each term inside parentheses.

Some problems, like number 7 $12x - (4x + 10) = 54$, require students to carefully manage negative signs and combine like terms before solving for the variable.

Highlight: The solutions provided demonstrate the importance of maintaining equation balance by performing the same operation on both sides of the equation.

This worksheet serves as excellent practice for students learning to solve increasingly complex equations, preparing them for more advanced algebraic concepts and problems with variables on both sides of the equation.