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Solve two-step equations Objective Solve two-step equations Example 4-4b

An equation that has two different operations Vocabulary Two-step equation An equation that has two different operations Example 4-4b

Example 1 Solve a Two-Step Equation Example 4 Use an Equation to Solve a Problem Lesson 4 Contents

Ask “what is being done to the variable first?” Write the equation. Solve Ask “what is being done to the variable first?” 4x is being added by 3 4x + 3 - 3 = 19 4x + 3 - 3 = 19 - 3 4x + 3 - 3 4x + 3 Do the inverse operation on each side Bring down 4x + 3 Subtract 3 Bring down = 19 Subtract 3 1/4 Example 4-1a

Use the Identify Property to add 4x + 0 Bring down 4x Solve Combine “like” terms Bring down = 4x + 3 - 3 = 19 - 3 Combine “like” terms 4x 4x + 0 = 4x + 0 = 16 4x + 0 Use the Identify Property to add 4x + 0 4x = 16 Ask “what is being done to the variable?” x is being multiplied by 4 Do the inverse operation on each side 1/4 Example 4-1a

Using the fraction bar, divide 4x by 4 Bring down 4x = 16 Solve Using the fraction bar, divide 4x by 4 4x + 3 - 3 = 19 - 3 Divide 16 by 4 4x + 0 = 16 Combine “like” terms 4x = 16 Bring down  x = 4x = 16 Combine “like” terms 4 4 Use the Identify Property to multiply 1  x 1  x = 4 1 1  x = x = 4 Answer: x = 4 1/4 Example 4-1a

Solve Answer: t = 7 1/4 Example 4-1b

Ask “what is being done to the variable first?” Write the equation. Solve Ask “what is being done to the variable first?” -3c is being added by 9 -3c + 9 - 9 = 3 -3c + 9 - 9 = 3 - 9 -3c + 9 -3c + 9 - 9 Do the inverse operation on each side Bring down -3c + 9 Subtract 9 Bring down = 3 Subtract 9 2/4 Example 4-2a

Use the Identify Property to add -3c + 0 -3c -3c + 0 = -6 -3c + 0 = Bring down -3c Combine “like” terms Solve Bring down = -3c + 9 - 9 = 3 - 9 Combine “like” terms Use the Identify Property to add -3c + 0 -3c -3c + 0 = -6 -3c + 0 = -3c + 0 -3c = -6 Ask “what is being done to the variable?” c is being multiplied by -3 Do the inverse operation on each side 2/4 Example 4-2a

Using the fraction bar, divide -3c by -3 Bring down -3c = -6 Solve Using the fraction bar, divide -3c by -3 Divide -6 by -3 -3c + 9 - 9 = 3 - 9 Combine “like” terms -3c + 0 = -6 -3c + 0 = -3c + 0 -3c Bring down  c = -3c = -6 Combine “like” terms -3c = -6 Use the Identify Property to multiply 1  c -3 -3 1 1  c = 2 1  c = c = 2 Answer: c = 2 2/4 Example 4-2a

Solve Answer: k = -3 2/4 Example 4-2b

Ask “what is being done to the variable first?” Write the equation. Solve Ask “what is being done to the variable first?” 3t is being added by 6 6 - 6 + 3t = 0 6 - 6 + 3t = 0 - 6 6 6 - 6 Do the inverse operation on each side Bring down 6 Subtract 6 Bring down + 3t = 0 Subtract 6 3/4 Example 4-3a

Use the Identify Property to add 0 + 3t Combine “like” terms Bring down +3t = Solve Combine “like” terms 6 - 6 + 3t = 0 - 6 Use the Identify Property to add 0 + 3t 0 + 3t = - 6 0 + 3t = Ask “what is being done to the variable?” 3t = - 6 t is being multiplied by 3 Do the inverse operation on each side 3/4 Example 4-3a

Do the inverse operation on each side Solve Bring down 3t = -6 Using the fraction bar, divide 3t by 3 6 - 6 + 3t = 0 - 6 Divide -6 by 3 0 + 3t = - 6 0 + 3t = Combine “like” terms 3t = - 6 Bring down  t = 3t = - 6 Combine “like” terms 3 3 Use the Identify Property to multiply 1  t 1 t = -2 1 1 t = t = -2 Answer: t = -2 3/4 Example 4-3a

Solve Answer: 8 = x 3/4 Example 4-3b

76,000 Georgia. three times the number There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi? 4,000 acres more than three times the number 76,000 = 76,000 = 3x + 4,000 76,000 Georgia has 76,000 acres “this is” refers to = Refers to + 4,000 Refers to 3x Solve the 2-step equation 4/4 Example 4-4a

76,000 Georgia. three times the number There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi? 4,000 acres more than three times the number Ask “what is being done to the variable first?” 76,000 = 3x + 4,000 76,000 - 4000 76,000 - 4000 = 3x + 4,000 76,000 76,000 - 4000 = 3x + 4,000 - 4,000 3x is being added by 4,000 Do the inverse operation on each side Bring down 76,000 Subtract 4,000 Bring down = 3x + 4,000 Subtract 4,000 4/4 Example 4-4a

76,000 Georgia. three times the number There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi? 4,000 acres more than three times the number Combine “like” terms 76,000 = 3x + 4,000 76,000 - 4000 = 3x + 4,000 - 4,000 72,000 = 3x 72,000 = 3x + 0 72,000 Bring down =3x 72,000 = 3x Combine “like” terms Use the Identify Property to add 3x + 0 4/4 Example 4-4a

76,000 Georgia. three times the number There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi? 4,000 acres more than three times the number Ask “what is being done to the variable?” 76,000 = 3x + 4,000 76,000 - 4000 = 3x + 4,000 - 4,000 72,000 = 3x 72,000 72,000 = 3x + 0 x is being multiplied by 3 72,000 = 3x Do the inverse operation on each side 72,000 = 3x Bring down 72,000 = 3x 3 Using the fraction bar, divide 72,000 by 3 4/4 Example 4-4a

76,000 Georgia. three times the number There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi? 4,000 acres more than three times the number Divide 3x by 3 76,000 = 3x + 4,000 76,000 - 4000 = 3x + 4,000 - 4,000 Combine “like” terms 72,000 = 3x + 0 72,000 = 3x 72,000 Bring down = 72,000 = 3x Combine “like” terms 72,000 = 3x Use the Identify Property to multiply 1  x 3 3 Answer: 24,000 acres = x 24,000 = 1  x 24,000 24,000 = 4/4 Example 4-4a

* BASEBALL Matthew had 64 hits during last year’s baseball season. This was 8 less than twice the number of hits Gregory had. How many hits did Gregory have during last year’s baseball season? Answer: x = 36 hits 4/4 Example 4-4b

Solving Two-Step Equations Assignment Lesson 4:4 Solving Two-Step Equations 8 - 31 All End of Lesson 4