Learn Equations And Inequalities | Two Step Equations

Key Concepts

• Write a two-step equation to represent a situation    
• Write more two step equations
• Interpret quantities and operations in equations

5.1 Write two-step equation 

Two-Step Equations Definition 

Equations that can be solved in exactly two-steps and give the final value of the variable in two steps are called two-step equations and are algebraic equations.  

Two step equations are of the form ax + b = c, where a, b, c are real numbers.  

An example of two-step equations is: 2x + 3 = 7 

Example: 

Write a two-step equation. 

Seven less than three times a number is twenty. 

Sol: 

Let n represent the number. 

Seven less – 7 

Three times a number 3n 

Is twenty =20 

3n -7 =20 

5.1.1 Write a Two-Step Equation to Represent a Situation  

Example1: 

Cole buys a new laptop for $335. He makes a down payment of $50 and pays the rest in 6 equal monthly payments, P. What equation represents the relationship between the cost of the laptop and Cole’s payments? 

Sol: 

Cost = down payment + six × monthly payment 

$335 = 50 + 6 × p 

$335 =6p +50 

The equation represents the relationship between the cost of the laptop and Cole’s payments= $335 =6p +50 

Example2: 

Kelvin had $70 in his bank account. After he bought 3 shirts that each cost the same amount, he had $52 in his account. How much did each shirt cost? Write an equation for this situation. 

Sol: 

Money Kelvin had in his bank account = $70 

x = cost of each shirt  

Shirts = 3 

70 – 3x =52 

5.1.2 Write More Two-Step Equations 

Example1: 

Charmin’s friend bought 3 bags of wild bird seed and an 18 bird feeder. Each bag of birdseed costs the same amount. If her friend spent $45, write an equation to find the cost of one bag of bird seed. 

Sol: 

C =cost of bag birdseed 

3C + 18 = 45 

Equation 3C +18 = 45 

5.1.3 Interpret Quantities and Operations in Equations 

Example 1: 

Ria bought 7 tickets for a total cost of $124. She had used a coupon code to get $4 off each ticket. Let x be the original cost of each ticket. Which of the following equations correctly represents the situation? 

1. 4(x-7) =124                 b.   7x – 4 =124 c.   7(x – 4) =124 

Sol: 

The equation 7(x – 4) = 124 represent this situation. 

Exercise

1. Write a problem that could be represented by the equation 5n -11=19.
2. Describe the situation that the equation could represent   g+3 / 6= 15.
3. Robert wrote the following description: three fewer than one-fourth of x is 12. Write an equation to represent the description.
4. Dalia bought a few swirl marbles and divided them equally among four of her friends and her brother, Jake. While playing, Jake lost 2 marbles and has only 7 marbles at present. Write an equation to represent the situation.
5. The Rock Zoo nurses 37 species of big cats. Recently, a few species of big cats were sponsored to other zoos around the country. The zoo now nurses only 25 species. Write an equation to represent how many species of big cats were sponsored to other zoos.
6. Melanie saves $20 every month in her savings account. She withdrew $60 one time to go shopping. She now has $280 in her account. Write an equation to determine how many months she has been saving.
7. Describe the situation that the equation could represent 

m/4  + 8 = 15.

• Describe the situation that the equation could represent    

x/ 4 + 4 = 10.

• Michelle is a server in a restaurant. On a weekend night, Michelle earned $4 an hour and $65 in tips. She made a total of $93. Write an equation to determine how many hours she worked.
• Write a problem that could be represented by the equation 3n – 3=9.

Concept Map

What have we learned:

• Understand two–step equations
• Understand how to write a two- step equation to represent a situatio
• Write more two step equations
• Interpret quantities and operations in equations