Solving First-Degree Equations Practice Problems - All Methods

Master solving linear equations using addition, subtraction, multiplication, division, combining like terms, and distributive property with step-by-step practice problems.

📚Practice Solving Equations Using Every Method You Need to Know

Solve equations by adding or subtracting the same number from both sides
Master multiplying and dividing both sides to eliminate coefficients and fractions
Combine like terms by moving variables to one side and constants to the other
Apply the distributive property to eliminate parentheses in linear equations
Work with equations containing variables on both sides of the equal sign
Build confidence solving first-degree equations with one variable step-by-step

Understanding Solving Equations Using All Methods

Complete explanation with examples

First-degree equation in one variable – solving by all methods

$2x-6=34$ Variable

A first-degree equation is an equation where the highest power is $1$ and there is only one variable $1$ .

Solving an Equation by Adding/Subtracting from Both Sides If the number is next to $X$ with a plus, we need to subtract it from both sides.
If the number is next to $X$ with a minus, we need to add it to both sides.

Solving an Equation by Multiplying/Dividing Both Sides We will need to multiply or divide both sides of the equations where there is a coefficient for $X$ .

Solving an Equation by Combining Like Terms Move all the $X$ s to the right side and all the numbers to the left side.

Solving an equation using the distributive property We will solve according to the distributive property
$a(b+c)=ab+bc$

Detailed explanation

Practice Solving Equations Using All Methods

Test your knowledge with 151 quizzes

Solve for X:

$$ x + 3 = 7 $$

Examples with solutions for Solving Equations Using All Methods

Step-by-step solutions included

Exercise #1

Solve for X:

$3x=18$

Step-by-Step Solution

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

Note that the coefficient of X is 3.

Therefore, we will divide both sides by 3:

$\frac{3x}{3}=\frac{18}{3}$

Then divide accordingly:

$x=6$

Answer:

$6$

Video Solution

Exercise #2

$x+7=14$

$x=\text{?}$

Step-by-Step Solution

To solve the equation $x + 7 = 14$ , we aim to find the value of $x$ by isolating it on one side.

Step 1: Identify the current equation: $x + 7 = 14$ .
Step 2: To isolate $x$ , perform the inverse operation. Subtract 7 from both sides to maintain equality.
Step 3: Simplify both sides: $x + 7 - 7 = 14 - 7$ .
Step 4: This simplifies to $x = 7$ .

Therefore, we have found that the solution to the equation $x + 7 = 14$ is $x = 7$ , which matches the given answer choice 2.

Answer:

Video Solution

Exercise #3

Solve for X:

$x - 7 = 14$

Step-by-Step Solution

To solve the equation $x - 7 = 14$ , we need to isolate $x$ .

Step 1: Add 7 to both sides of the equation to cancel out the -7 on the left side.
$x - 7 + 7 = 14 + 7$
Step 2: Simplify both sides.
$x = 21$
Thus, the solution is $x = 21$ .

Answer:

$21$

Exercise #4

Solve for X:

$x + 9 = 3$

Step-by-Step Solution

To solve the equation $x + 9 = 3$ , we need to isolate $x$ .

Step 1: Subtract 9 from both sides of the equation to cancel out the +9 on the left side.
$x + 9 - 9 = 3 - 9$
Step 2: Simplify both sides.
$x = -6$
Thus, the solution is $x = -6$ .

Answer:

$-6$

Exercise #5

Solve for X:

$x - 5 = -10$

Step-by-Step Solution

To solve the equation $x - 5 = -10$ , we need to isolate $x$ .

Step 1: Add 5 to both sides of the equation to cancel out the -5 on the left side.
$x - 5 + 5 = -10 + 5$
Step 2: Simplify both sides.
$x = -5$
Thus, the solution is $x = -5$ .

Answer:

$-5$

Frequently Asked Questions

Everything you need to know about Solving Equations Using All Methods

What is a first-degree equation with one variable?

A first-degree equation with one variable is an equation where the highest power of the variable is 1 and contains only one variable (usually x). Examples include 3x + 5 = 20 or 4(x + 2) - 2x = 12. The goal is to find the value of x that makes the equation true.

When do I add or subtract from both sides of an equation?

Add or subtract from both sides to isolate the variable. If a number is added to x (like x + 7), subtract that number from both sides. If a number is subtracted from x (like x - 4), add that number to both sides. This keeps the equation balanced while moving terms.

How do I solve equations with coefficients or fractions?

For coefficients (like 2x = 12), divide both sides by the coefficient to isolate x. For fractions (like x/4 = 5), multiply both sides by the denominator to eliminate the fraction. Always perform the same operation on both sides to maintain equality.

What does combining like terms mean in equations?

Combining like terms means moving all variable terms to one side and all constant numbers to the other side. For example, in 5x - 3 = 2x + 9, move the x terms to get 5x - 2x = 9 + 3, then simplify to 3x = 12.

When do I use the distributive property in equations?

Use the distributive property when you see parentheses in an equation, like 2(x + 3) = 14. Apply a(b + c) = ab + ac to get 2x + 6 = 14, then solve normally. This eliminates parentheses and simplifies the equation.

What are the steps to solve any first-degree equation?

Follow these steps in order: 1) Use distributive property to eliminate parentheses, 2) Combine like terms on each side, 3) Move all variable terms to one side and constants to the other, 4) Divide both sides by the coefficient of the variable. Always check your answer by substituting back into the original equation.

How do I check if my solution to an equation is correct?

Substitute your answer back into the original equation and verify both sides are equal. For example, if you solved 2x - 6 = 34 and got x = 20, check: 2(20) - 6 = 40 - 6 = 34 ✓. If both sides equal the same number, your solution is correct.

What's the difference between solving 2x = 8 and x/2 = 4?

For 2x = 8, divide both sides by 2 to get x = 4. For x/2 = 4, multiply both sides by 2 to get x = 8. When the variable is multiplied by a number, divide by that number. When the variable is divided by a number, multiply by that number.

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Master Solving Equations Using All Methods first, then advance to these related topics that build on your fraction skills

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Solving First-Degree Equations Practice Problems - All Methods

Understanding Solving Equations Using All Methods

First-degree equation in one variable – solving by all methods

Practice Solving Equations Using All Methods

Examples with solutions for Solving Equations Using All Methods

Frequently Asked Questions

What is a first-degree equation with one variable?

When do I add or subtract from both sides of an equation?

How do I solve equations with coefficients or fractions?

What does combining like terms mean in equations?

When do I use the distributive property in equations?

What are the steps to solve any first-degree equation?

How do I check if my solution to an equation is correct?

What's the difference between solving 2x = 8 and x/2 = 4?

More Solving Equations Using All Methods Questions

Solving Equations Using All Methods

Solving an Equation by Multiplication/ Division

Solving Equations by using Addition/ Subtraction

Simplifying and Combining Like Terms

Solving Quadratic Equations using Factoring

Continue Your Math Journey

Suggested Topics to Practice in Advance

Topics Learned in Later Sections

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