Unit 3 Day 5

Solving Equations with the Variable on

Each Side

Common Core State Standards A.REI.1 Explain each step in solving a simple equations as following form the

equality of numbers asserted at the previous step, starting fr0m the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Mathematical Practices 1. Make sense of problems and persevere in solving them. 5. Use appropriate tools strategically.

To solve an equation that

has variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variable on one side.

Variables on Each Side

Solve an Equation with Variables on Each SideSolve . Check your solution.

Example 1

Solve each equation. Check your

solution.1A. 1B.

Guided Practice

Solve each equation. Check your

solution.1C. 1D.

Guided Practice

If equations contain

grouping symbols such as parentheses or brackets, use the Distributive Property first to remove the grouping symbols.

Grouping Symbols

Solve an Equation with Grouping SymbolsSolve .

Example 2

Solve each equation. Check your

solution.2A. 2B.

Guided Practice

Some equations may have

no solution. That is, there is no value of the variable that will result in a true equation. Some equations are true for all values of the variables. These are called identities.

Find Special SolutionsSolve each equation.a.

Example 3

Find Special SolutionsSolve each equation.b.

Example 3

3A.

Guided Practice

3B.

Guided Practice

STEP 1 Simplify the expressions on each

side. Use the Distributive Property as needed.

STEP 2 Use the Addition and/or Subtraction Property of Equality to get the variables on one side and the numbers without variables on the other side. Simplify.

STEP 3 Use the Multiplication or Division Property of Equality to solve.

Summary Steps for Solving Equations

Write an equation.Find the value of x so that the figures have the same area.

Example 4

10 cm

x cm

3 cm x cm

6 cm

4. Find the value of x so that the figures

have the same perimeter.

Guided Practice

x

6

x

2x +2

1. Determine whether each solution is

correct. If the solution is not correct, find the error and give the correct solution.

a. 2 2

Check For Understanding

1. Determine whether each solution is

correct. If the solution is not correct, find the error and give the correct solution.

b. 3d = 3 3 d =

Check For Understanding

1. Determine whether each solution is

correct. If the solution is not correct, find the error and give the correct solution.

c. 13 = z

Check For Understanding

Solve each equation.

2. 3.

4. 5.

6. 7.

Check for Understanding

Solve each equation.2. 3. 4 34. 5. no solution 6. 7. all real numbers 2.5

Check for Understanding

Solving Equations Involving Absolute Value

Common Core State Standards A.REI.1 Explain each step in solving a simple equations as following form

the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Mathematical Practices 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

Expressions with absolute

values define an upper and lower range in which a value must lie. Expressions involving absolute value can be evaluated using the given value for the variable.

Absolute Value Expressions

Expressions with Absolute ValueEvaluate if m = 4.

Example 1

1. Evaluate if x = 2.

Guided Practice

There are three types of open sentences

involving absolute value, , and . In this lesson, we will consider only the first type. Look at the equation . This means that the distance between 0 and x is 4.

If , then or . Thus, the solution set is

Absolute Value Equations

For each absolute value

equation, we must consider both cases. To solve an absolute value equation, first isolate the absolute value on one side of the equals sign if it is not already by itself.

Absolute Value Equations

Words When solving equations that

involve absolute values, there are two cases to consider.

Case 1 The expression inside the absolute value symbol is positive or zero.

Case 2 The expression inside the absolute value symbol is negative.

Symbols For any real numbers a and b, if and , then or .

Example , so or

Key Concept:Absolute Value Equations

Solve Absolute Value EquationsSolve each equation. a. =17 b.

Example 2

2A. 2B.

Guided Practice

Solve an Absolute Value EquationSNAKES The temperature of an enclosure for a pet snake should be about 80F, give or take 5. Find the maximum and minimum temperatures.

Real-World Example 3

ICE CREAM Ice Cream should be stored at 5F

with an allowance for 5. Write and solve an equation to find the maximum and minimum temperatures at which the ice cream should be stored.

Guided Practice

Example 1 – Evaluate each expression if f = 3,

g = , and h =5.

1. 2. 3.

Check For Understanding

Example 1 – Evaluate each expression if f = 3,

g = , and h =5.

1. 2. 3. 15 11

Check For Understanding

Example 2 – Solve each equation.

4. 5. 6. 6

7. 8. 9.

Check For Understanding

Example 2 – Solve each equation.

4. 5. 6. 6

7. 8. 9.

Check For Understanding