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Practice Problems
Solve for x
\(\textbf{1)}\) \(3x+2=14\)
\(\textbf{2)}\) \(5x-2=8\)
\(\textbf{3)}\) \(\displaystyle\frac{x}{3}-7=2\)
\(\textbf{4)}\) \(\displaystyle\frac{x}{5}+2=4\)
\(\textbf{5)}\) \(\displaystyle\frac{x+2}{3}=2\)
\(\textbf{6)}\) \(\displaystyle\frac{x-4}{5}=2\)
\(\textbf{7)}\) \(3x+5=7x-3\)
\(\textbf{8)}\) \(2x-1=4x-5\)
\(\textbf{9)}\) \(\displaystyle\frac{x}{5}+\displaystyle\frac{x}{6}=11\)
\(\textbf{10)}\)\(\displaystyle\frac{x}{2}+\displaystyle\frac{x}{3}=5\)
\(\textbf{11)}\) \(4− (2− 3x) = 9\)
\(\textbf{12)}\) \(3(2x+5)-4(x-1)=23\)
\(\textbf{13)}\) \(2(3x+5)-3(4x-3)=13\)
\(\textbf{14)}\) \(2x-5=10\)
Challenge Problems
Solve for z
\(\textbf{15)}\) \(zx+ry=n\)
\(\textbf{16)}\) \(zx+zny=m\)
See Related Pages\(\)
\(\bullet\text{ Equation Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Equation Solver Calculator (Symbolab.com)}\)
\(\,\,\,\,\,\,\,\,2x+5=11…\)
\(\bullet\text{ Solving Equations by Addition and Subtraction}\)
\(\,\,\,\,\,\,\,\,x+3=4…\)
\(\bullet\text{ Solving Equations by Multiplication and Division}\)
\(\,\,\,\,\,\,\,\,8x=48…\)
\(\bullet\text{ Solving Multi-step Equations}\)
\(\,\,\,\,\,\,\,\,3x+2=14…\)
\(\bullet\text{ Solving Equations with Variables on Both Sides}\)
\(\,\,\,\,\,\,\,\,3x+5=7x-3…\)
\(\bullet\text{ Solving Equations with Decimals}\)
\(\,\,\,\,\,\,\,\,43.5+0.2x=51.1…\)
\(\bullet\text{ Solving Equations with Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}…\)
\(\bullet\text{ Andymath Homepage}\)
In Summary
Solving equations involves finding the value of a variable by manipulating and rearranging algebraic equations with multiple steps. These equations typically have multiple terms on one or both sides of the equal sign and may involve the use of the distributive property and combining like terms. Learning about solving equations is important because it helps us understand how to solve real-world problems involving algebra. It also helps us develop critical thinking and problem-solving skills, which are valuable in many different fields.
Real world examples of Solving Equations
A carpenter is building a bookshelf that is 8 feet long. The carpenter wants to divide the bookshelf into 3 equal sections. How long should each section be?
A store is selling bags of apples for $4 each. If a customer buys 7 bags, how much will they spend in total?
A runner runs a total of 20 miles in 5 days. On average, how many miles does the runner run per day?
A swimmer swims a total of 50 laps in a pool that is 25 meters long. How far did the swimmer swim in total?
A baker needs to bake a cake that serves 12 people. If the baker only has enough ingredients to make a cake that serves 9 people, how much more of each ingredient does the baker need to buy?
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!
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