# Write And Solve Linear Equations With Variables On Both Sides (Word Problems) Worksheet

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Writing and solving linear equations with variables on both sides involves translating real-world situations into mathematical expressions and then finding the solution. By understanding the problem, defining variables, and setting up equations, you can efficiently solve for the unknowns and obtain understanding of the underlying connections within the context of the problem. In these worksheets, students need to find the equation and solve for the variable for the given word problem.

Algebra 1
One-Variable Equations

## How Will This Worksheet on "Write and Solve Linear Equations with Variables on Both Sides (Word Problems)" Benefit Your Students' Learning?

• Boosts your ability to think critically by using algebra in everyday situations.
• Gets better at solving problems by simplifying tricky word problems into easy steps.
• Build up your algebra skills by learning to balance equations with variables on both sides.
• Supports mathematical communication by translating verbal descriptions into algebraic expressions and vice versa.

## How to Write and Solve Linear Equations with Variables on Both Sides (Word Problems)?

• Read the word problem carefully and determine the quantities or variables that are unknown and need to be solved for.
• Assign variables to represent the unknown quantities. Typically, use letters like $$x$$, $$y$$, or other letters as needed.
• Express the information given in the problem as mathematical equations. Pay attention to keywords such as "more than," "less than," "twice as much as," etc., to determine the mathematical operations needed.
• Write linear equations that represent the relationships between the variables. Ensure that the equations accurately represent the given information in the problem.
• Arrange the equations so that all variables are on one side and constants are on the other side. This may involve combining like terms and simplifying expressions.
• Use appropriate algebraic techniques such as addition, subtraction, multiplication, and division to isolate and solve the variable.

## Solved Example

Q. Twin Rivers has a population of $90,800$, and its population has been increasing by $800$ people each year. White Stone has a population of $87,200$, and its population has been increasing by $1,200$ people each year. These trends in population change are expected to continue.$\newline$How long will it take for the two cities to have the same population?$\newline$Simplify any fractions.$\newline$____ years$\newline$
Solution:
1. Set Up Equation: Let's set up an equation to represent the populations of Twin Rivers and White Stone after $t$ years. We'll let $P_{\text{twin}}$ and $P_{\text{white}}$ represent the populations of Twin Rivers and White Stone, respectively, after $t$ years.$\newline$$P_{\text{twin}} = 90,800 + 800t$$\newline$$P_{\text{white}} = 87,200 + 1,200t$$\newline$We want to find the value of $t$ when $P_{\text{twin}} = P_{\text{white}}$.
2. Equalize Populations: Now we set the two expressions equal to each other to find when the populations will be the same: $90,800 + 800t = 87,200 + 1,200t$$\newline$
3. Solve for t: To solve for t, we need to get all the terms with $t$ on one side and the constants on the other side. Let's subtract $800t$ from both sides:$\newline$$90,800 + 800t - 800t = 87,200 + 1,200t - 800t$$\newline$This simplifies to:$\newline$$90,800 = 87,200 + 400t$
4. Subtract Constants: Next, we subtract $87,200$ from both sides to isolate the term with $t$: $\newline$$90,800 - 87,200 = 87,200 + 400t - 87,200$$\newline$This simplifies to:$\newline$$3,600 = 400t$
5. Divide by $400$: Now we divide both sides by $400$ to solve for $t$: $\newline$$\frac{3,600}{400} = \frac{400t}{400}$$\newline$This simplifies to:$\newline$$t = 9$

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