One-Step Equations with Rational Coefficients

Warm Up -2x = 34 y – 3.5 = -2.1 2 3 𝑧=−6 -4x = -4.8 − 1 4 𝑥=−4.8

Inverse operations “undo” each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. When solving an equation, the inverse operation must be performed on both sides of the equal sign to maintain the equality. To solve an equation, it is necessary to isolate the variable.

A solution of an equation is the value of the variable that makes the equation true. Operations that undo each other, such as addition and subtraction, and multiplication and division, are called inverse operations. Inverse operations are used to solve equations. To solve an equation, the operation performed on the variable must be undone, leaving the variable alone, or isolated, on one side of the equation. The value on the other side of the equal sign should be the solution of the equation, if the solution process was performed properly.

Does it matter which side of the equation the variable is on? How do you check that a solution is correct?

What is the product when you multiply a fraction by its reciprocal? Consider the equation 3 4 𝑥=5 x is being multiplied by 3 4 . The inverse of multiplication is division. Why do we solve this equation by multiplying by the reciprocal of 3 4 instead of dividing by 3 4 ?

A store is having a sale. The price of a jacket is set to decrease by $1.50 during each hour of the sale. How long will it take for the price of the jacket to decrease by $18?

Solve x – 5.6 = -1.7 y + 3 4 = 6 0.7n = -3.5 𝑐 2.5 = -4.2 -8.5 + x = -2

Amy has some money in her checking account Amy has some money in her checking account. If she writes a check for $42.50, her checking account will be overdrawn by $23.75. Find how much money is in Amy’s checking account now.

Tyler received a notice from his bank that the balance in his checking account was –$12, not $0 as he expected. He realized that he forgot to record the time when he used his debit card to buy bus tokens for $1.50 each. How many bus tokens did Tyler buy?

Between the hours of 10 P. M. and 6 A. M Between the hours of 10 P.M. and 6 A.M., the temperature decreases an average of 𝟑 𝟒 of a degree per hour. How long, in hours, will it take for the temperature to decrease by 5 °F?

Which operations are inverses of each other Which operations are inverses of each other? Why must we perform the same operation on both sides of the equation when isolating the variable?

Solve the equations in order Solve the equations in order. Use the value of the variables you find in each of the following equations. 1. Solve for a: 3a = -4.2 2. Solve for b: a + b = -7.8 3. Solve for c: 1 2 3 c = a-b 4. Solve for d: 𝑎+𝑏 𝑐 =−2𝑑

Exit Ticket a - 5 6 = -3 2 3 3. − 𝟑 𝟓 d = 15 k + 7.2 = 3.4 4. 𝒘 −𝟏.𝟑 = -6.2 The height of the water in an above ground pool is 3 feet. The pool needs to be drained. As the water drains, the height of the water changes at a rate of − 1 2 inch per minute. Write and solve an equation to find how many minutes it will take to drain the pool. The melting point of the chemical bromine is -7.2 °C. The boiling point of bromine is 58.8 °C. Write and solve an equation to find how much greater the boiling point of bromine is than the melting point.