Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?
Solve for x
\(\textbf{1)}\) \(\displaystyle\frac{1}{3}x+5=8\)
\(\textbf{2)}\) \(\displaystyle\frac{2}{5}x+\displaystyle\frac{2}{3}=\displaystyle\frac{8}{3}\)
\(\textbf{3)}\) \(\displaystyle\frac{1}{3}x-\displaystyle\frac{9}{2}=\displaystyle\frac{9}{2}\)
\(\textbf{4)}\) \(\displaystyle\frac{4}{7}+x=2\)
\(\textbf{5)}\) \(\displaystyle\frac{3}{5}x-\frac{2}{3}=\frac{1}{5}\)
\(\textbf{6)}\) \(\displaystyle\frac{x}{3}-7=2\)
\(\textbf{7)}\) \(\displaystyle\frac{x}{5}+\displaystyle\frac{x}{6}=11\)
\(\textbf{8)}\) \(\displaystyle\frac{1}{4}x+\frac{1}{3}=\frac{5}{6}\)
\(\textbf{9)}\) \(\displaystyle\frac{1}{5}x+\frac{1}{2}=\frac{7}{10}\)
\(\textbf{10)}\) \(\displaystyle\frac{1}{5}x+\frac{2}{15}=\frac{7}{3}\)
\(\textbf{11)}\) \(\displaystyle\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}+2\)
See Related Pages\(\)
\(\bullet\text{ Equation Calculator (Symbolab.com)}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Solving Equations by Addition and Subtraction}\)
\(\,\,\,\,\,\,\,\,x+3=4…\)
\(\bullet\text{ Solving Equations by Multiplication and Division}\)
\(\,\,\,\,\,\,\,\,8x=48…\)
\(\bullet\text{ Solving Multi-step Equations}\)
\(\,\,\,\,\,\,\,\,3x+2=14…\)
\(\bullet\text{ Solving Equations with Variables on Both Sides}\)
\(\,\,\,\,\,\,\,\,3x+5=7x-3…\)
\(\bullet\text{ Solving Equations with Decimals}\)
\(\,\,\,\,\,\,\,\,43.5+0.2x=51.1…\)
\(\bullet\text{ Solving Equations with Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}…\)
In Summary
Solving equations is an essential part of algebra, and it involves finding the value of an unknown variable that makes an equation true. This involves using the properties of equality, such as the addition and multiplication properties, to isolate the unknown variable and determine its value.
We learn about solving equations because they are a fundamental part of mathematics and are used in many different fields, such as science, engineering, and economics. By understanding how to solve equations, we can better understand and analyze real-world problems and make more informed decisions.
Solving equations is typically taught in high school algebra classes, which is the first course in a series of college-preparatory math classes. It is usually taught in the context of linear equations, which are equations that have the form “ax + b = c,” where a, b, and c are constants and x is the unknown variable.
One common mistake when solving equations is failing to use the correct order of operations. For example, \(3x+2=8\) You need to subtract the \(2\) from both sides before dividing both sides by \(3\).
A fun fact about solving equations is that they were first used in ancient civilizations to solve practical problems, such as finding the dimensions of a field or the amount of money owed in a transaction. In fact, the ancient Egyptians and Babylonians were some of the first civilizations to use equations to solve problems.
Some related topics to solving equations include linear algebra, quadratic equations, and systems of equations. Linear algebra involves solving systems of linear equations, while quadratic equations are equations that have an x^2 term and can be solved using methods such as factoring or the quadratic formula. Systems of equations involve solving multiple equations simultaneously, and they can be solved using methods such as graphing or substitution.
Topics that use Solving Equations
Algebraic expressions and equations: Solving equations is an important part of algebra.
Geometry: In geometry, equations are used to solve problems involving lengths, angles, and areas.
Trigonometry: Trigonometry is the study of the relationships between the sides and angles of triangles. Solving equations is often used to find unknown values in trigonometry problems.
Calculus: Calculus is the study of rates of change and involves the use of derivatives and integrals. Solving equations is used to find the values of these derivatives and integrals.
Differential equations: A differential equation is an equation that relates an unknown function and its derivatives. Solving differential equations is used in many areas of math and science, such as physics, engineering, and economics.
About Andymath.com
Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.
Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
Visit me on Youtube, Tiktok, Instagram and Facebook. Andymath content has a unique approach to presenting mathematics. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. We are open to collaborations of all types, please contact Andy at tutoring@andymath.com for all enquiries. To offer financial support, visit my Patreon page. Let’s help students understand the math way of thinking!
Thank you for visiting. How exciting!