One-Step Equations with Rational Coefficients

Warm Up1. -2x = 34

2. y – 3.5 = -2.1

3. -4x = -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

x is being multiplied by . The inverse of multiplication is division.

Why do we solve this equation by multiplying by the reciprocal of instead of dividing by ?

A store is having a sale.The price of a jacket is set to

decrease by $1.50 during eachhour of the sale. How long will it

take for the price of thejacket to decrease by $18?

Solve

x – 5.6 = -1.7 y + = 6

0.7n = -3.5 = -4.2

-8.5 + x = -2

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 accountnow.

Tyler received a notice from his bankthat the balance in his checkingaccount was –$12, not $0 as he

expected. He realized that he forgot torecord the time when he used his

debit card to buy bus tokens for $1.50each. How many bus tokens did Tyler

buy?

Between the hours of 10 P.M. and 6 A.M., the temperature

decreases anaverage of of a degree per hour.

How long, in hours, will ittake for the temperature to

decrease by 5 °F?

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. Use the value of the variables you find in each of the following equations.

1. Solve for a: 3a = -4.22. Solve for b: a + b = -7.83. Solve for c: c = a-b4. Solve for d:

Exit Ticket1. a - = -3 3. d = 15

2. k + 7.2 = 3.4 4. = -6.2

5. 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 inch per minute. Write and solve an equation to find how many minutes it will take to drain the pool.

6. 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.