Equation Unknown Practice Problems - Solve for Variables

Master solving equations with unknowns through step-by-step practice problems. Learn to isolate variables using addition, subtraction, multiplication, and division operations.

📚Master Solving Equations with Unknown Variables

Identify unknown variables (X, Y) in algebraic equations
Apply inverse operations to isolate variables step-by-step
Solve linear equations by adding and subtracting terms
Clear coefficients using multiplication and division
Handle equations with variables on both sides
Determine when equations are undefined or have no solution

Understanding Equation (+ what is the unknown)

Complete explanation with examples

But before explaining what unknowns are, it is important that we review the concept of what a mathematical equation is:

An equation is an algebraic expression that includes numbers (fixed values), and also letters with unknown value (unknowns). Our goal is to arrive at a solution to the equation, that is, to find the missing value (the unknown), so that both sides of the equation are equal.

What is an unknown?

In general, we express the unknowns with the letters $X$ , $Y$ or Greek letters such as alpha and beta. Most of the time we will be asked to find the unknown value to be determined by solving an equation.

Labeled algebraic equation illustrating parts of an expression: terms, coefficients, variables, constants, and the full equation, using color-coded annotations for clarity.

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 an unknown in a math equation?

An unknown is a variable (usually represented by letters like X or Y) whose value needs to be found to make both sides of the equation equal. It represents the missing number that solves the equation.

How do you solve for an unknown variable in an equation?

To solve for an unknown variable, use inverse operations to isolate the variable on one side of the equation. This involves: 1) Add or subtract terms from both sides, 2) Multiply or divide both sides by the same number, 3) Simplify until the variable stands alone.

What are the steps to solve X + 5 = 8?

Step 1: Subtract 5 from both sides: X + 5 - 5 = 8 - 5. Step 2: Simplify: X = 3. Always perform the same operation on both sides to maintain equality.

How do you clear a coefficient from an unknown variable?

To clear a coefficient (number multiplying the variable), divide both sides of the equation by that coefficient. For example, in 14x = 14, divide both sides by 14 to get x = 1.

What makes an equation with unknowns undefined?

An equation becomes undefined when the denominator of a fraction equals zero. For example, in (25a + 4b)/(7y + 14) = 9b, the equation is undefined when y = -2 because it makes the denominator zero.

Can an unknown variable equal zero in an equation?

Yes, an unknown variable can equal zero. For instance, in 5x = 0, the solution is x = 0 because any number multiplied by zero equals zero.

How do you solve equations with variables on both sides?

Move all variable terms to one side and constants to the other side using addition or subtraction. Then combine like terms and solve for the variable using inverse operations.

What are the most common letters used for unknown variables?

The most commonly used letters for unknown variables are X and Y in basic algebra. Greek letters like alpha (α) and beta (β) are also used in more advanced mathematics.

Continue Your Math Journey

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