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?