



By the end of this section, you will be able to:
 Solve equations using a general strategy
 Classify equations
Before you get started, take this readiness quiz.
 Simplify:
$\text{\u2212}(a4).$
If you missed this problem, review
[link] .
 Multiply:
$\frac{3}{2}\left(12x+20\right)$ .
If you missed this problem, review
[link] .
 Simplify:
$52(n+1)$ .
If you missed this problem, review
[link] .
 Multiply:
$3(7y+9)$ .
If you missed this problem, review
[link] .
 Multiply:
$\left(2.5\right)\left(6.4\right)$ .
If you missed this problem, review
[link] .
Solve equations using the general strategy
Until now we have dealt with solving one specific form of a linear equation. It is time now to lay out one overall strategy that can be used to solve any linear equation. Some equations we solve will not require all these steps to solve, but many will.
Beginning by simplifying each side of the equation makes the remaining steps easier.
General strategy for solving linear equations.

Simplify each side of the equation as much as possible.
Use the Distributive Property to remove any parentheses.
Combine like terms.

Collect all the variable terms on one side of the equation.
Use the Addition or Subtraction Property of Equality.

Collect all the constant terms on the other side of the equation.
Use the Addition or Subtraction Property of Equality.

Make the coefficient of the variable term to equal to 1.
Use the Multiplication or Division Property of Equality.
State the solution to the equation.

Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.
Questions & Answers
Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio.
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B.
120 * TV
100= commission
12,000+
17,000 = of company a salary
29,000
17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B.
120 * TV
100= commission
12,000+
17,000 = of company a salary
29,000
Ciid
I'm mathematics teacher from highly recognized university.
is anyone else having issues with the links not doing anything?
chapter 1 foundations 1.2 exercises variables and algebraic symbols
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold? Enter the answers in decimal form.
Joseph would like to make 12 pounds of a coffee blend at a cost of $6.25 per pound. He blends Ground Chicory at $4.40 a pound with Jamaican Blue Mountain at $8.84 per pound. How much of each type of coffee should he use?
Samer
4x6.25= $25 coffee blend 4×4.40= $17.60 ground chicory 4x8.84= 35.36 blue mountain. In total they will spend for 12 pounds $77.96 they will spend in total
tyler
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for threequarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.
i need help how to do this is confusing
what kind of math is it?
Danteii
huh, what is the algebra problem
Daniel
How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths many sailors as soldiers?
tyler
What is the domain and range of heaviside
What is the domain and range of Heaviside and signum
Christopher
The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle.
Tickets for a show are $70 for adults and $50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled $17,200. How many adult tickets and how many child tickets were sold?
A 50% antifreeze solution is to be mixed with a 90% antifreeze solution to get 200 liters of a 80% solution. How many liters of the 50% solution and how many liters of the 90% solution will be used?
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?
Washing his dad’s car alone, eightyearold Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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