# Create and Solve Equations and Inequalities

Examples, solutions, videos, and lessons to help High School students learn how to create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

### Suggested Learning Targets

• Create linear, quadratic, rational and exponential equations and inequalities in one variable and use them in a contextual situation to solve problems.

Common Core: HSA-CED.A.1

Create equations and inequalities in one variable and use them to solve problems (A-CED.1)
How to write an equation from a word problem?
Example:
A company buys a trucks at b dollars per truck and c tons of plastic at d dollars for each ton. It spends a total of T dollars, where T = ab + cd. Write an equation for the situation presented.
Find the number of tons of plastic the company can afford to buy if it spends a total of \$200 million, plastic costs \$700 per ton, and it must buy 15 trucks at a price of \$3 million each. How many tons of plastic can the company afford? Round to the nearest unit the company can afford.

How to write an equation from a diagram?
Example:
Write the equation that shows that the top line is the same length as the bottom line. When presenting your final answer, combine all like terms.

How to create an expression from a word problem?
Example:
A shop sells twelve hotdogs and twenty bottles of soda for every baseball cap sold. Write an expression to determine the total number of items sold.

How to create an inequality from a word problem?

Solving One-Step Linear Equations

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.