Variable Practice Problems: Solve Equations and Word Problems

Master variables in algebra with step-by-step practice problems. Learn to identify dependent and independent variables, solve equations, and tackle real-world word problems.

📚Master Variables Through Interactive Practice

Identify and define variables using Latin letters like X, Y, and Z
Distinguish between dependent and independent variables in functions
Substitute values into algebraic expressions with multiple variables
Convert word problems into algebraic equations using variables
Solve real-world problems involving prices, quantities, and unknown values
Apply variable concepts to functions like Y = X² + 2X + 6

Understanding Equation (+ what is the unknown)

Complete explanation with examples

Variable

What is a variable?

A variable is a specific symbol like a Latin letter – $X$ / $Y$ / $Z$ that can change and represent a quantity/value.

Solving simple algebraic equations: X + 5 = 8 and Y = 3 - 1. The values of X and Y are determined step by step, highlighting basic arithmetic operations.

Detailed explanation

Practice Equation (+ what is the unknown)

Test your knowledge with 1 quizzes

$$ 5x=1 $$

What is the value of x?

Examples with solutions for Equation (+ what is the unknown)

Step-by-step solutions included

Exercise #1

$5x=0$

Step-by-Step Solution

To solve the equation $5x = 0$ for $x$ , we will use the following steps:

Step 1: Identify that the equation is $5x = 0$ .
Step 2: To solve for $x$ , divide both sides of the equation by 5.

Let's perform the calculation as outlined in Step 2:

$5x = 0$

Divide both sides by 5 to isolate $x$ :

x = \frac{0}{5}

Simplifying, this gives:

$x = 0$

Therefore, the solution to the equation $5x = 0$ is $x = 0$ .

The correct answer is option 4: $x = 0$ .

Answer:

$x=0$

Video Solution

Exercise #2

$5x=1$

What is the value of x?

Step-by-Step Solution

To solve the equation $5x = 1$ , we need to isolate $x$ . Here are the steps:

Step 1: Start with the equation $5x = 1$ .
Step 2: Divide both sides of the equation by the coefficient of $x$ , which is 5, to isolate $x$ . This gives us:

\frac{5x}{5} = \frac{1}{5}

Step 3: Simplify the left side:

\frac{5x}{5} = x

Step 4: Write the simplified equation:

x = \frac{1}{5}

Therefore, the solution to the equation $5x = 1$ is $x = \frac{1}{5}$ .

The correct answer choice is:

$x = \frac{1}{5}$

Answer:

$x=\frac{1}{5}$

Video Solution

Exercise #3

$14x+3=17$

$x=\text{?}$

Step-by-Step Solution

To solve the equation $14x + 3 = 17$ , we need to find the value of $x$ that satisfies the equation.

Step 1: Isolate the term containing $x$ by subtracting 3 from both sides of the equation:

$14x + 3 - 3 = 17 - 3$
This simplifies to:
$14x = 14$

Step 2: Solve for $x$ by dividing both sides by 14:

$x = \frac{14}{14}$
Which simplifies to:
$x = 1$

Therefore, the solution to the equation $14x + 3 = 17$ is $x = 1$ .

Answer:

$x=1$

Video Solution

Exercise #4

Solve the following problem:

$2x+7-5x-12=-8x+3$

Step-by-Step Solution

In order to solve this exercise, we first need to identify that we have an equation with an unknown.

To solve such equations, the first step will be to arrange the equation so that on one side we have the numbers and on the other side the unknowns.

$2X+7-5X-12=-8X+3$

First, we'll move all unknowns to one side.
It's important to remember that when moving terms, the sign of the number changes (from negative to positive or vice versa).

$2X+7-5X-12+8X=3$

Now we'll do the same thing with the regular numbers.

$2X-5X+8X=3-7+12$

In the next step, we'll calculate the numbers according to the addition and subtraction signs.

$2X-5X=-3X$
$-3X+8X=5X$

$3-7=-4$
$-4+12=8$

$5X=8$

At this stage, we want to reach a state where we have only one $X$ , not $5X$ ,
Thus we'll divide both sides of the equation by the coefficient of the unknown (in this case - 5).

$X={8\over5}$

Answer:

$x=\frac{8}{5}$

Video Solution

Frequently Asked Questions

Everything you need to know about Equation (+ what is the unknown)

What is a variable in math and how do I identify one?

A variable is a symbol (usually a Latin letter like X, Y, or Z) that represents an unknown quantity or value that can change. You can identify variables as letters that appear in mathematical expressions, equations, or functions where their value is not fixed.

What's the difference between dependent and independent variables?

An independent variable (usually X) can take any value within its range and doesn't depend on other variables. A dependent variable (usually Y) changes based on the value of the independent variable, like in the function Y = X² + 2X + 6.

How do I solve equations when the same variable appears multiple times?

When the same variable appears multiple times in an equation, it has the same value in all occurrences. Substitute the given value for every instance of that variable, then follow order of operations to solve.

What are the steps to convert word problems into algebraic equations?

1. Identify what you need to find and assign it a variable 2. Read the problem carefully to find relationships between quantities 3. Express these relationships using mathematical operations 4. Set up an equation that represents the problem situation

How do I substitute values into expressions with variables?

Replace every occurrence of the variable with the given number, keeping the same mathematical operations. For example, if X = 2 in Y = X² + 2X + 6, substitute to get Y = 2² + 2(2) + 6 = 4 + 4 + 6 = 14.

Can variables represent things other than numbers in word problems?

Yes! Variables can represent quantities like prices (X dollars), amounts (Y shirts), measurements (Z meters), or any unknown value. The key is clearly defining what each variable represents in the context of the problem.

What common mistakes should I avoid when working with variables?

Avoid these mistakes: treating the same variable as different values in one problem, forgetting to substitute values into all instances of a variable, and mixing up dependent vs independent variables in functions.

How do variables help solve real-world math problems?

Variables let you represent unknown quantities in real situations, like calculating total costs when prices vary, finding optimal solutions, or modeling relationships between different factors. They bridge the gap between abstract math and practical applications.

Continue Your Math Journey

Master Equation (+ what is the unknown) first, then advance to these related topics that build on your fraction skills

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