Lesson 2-4: Solving Multi-Step
Equations
Algebra 1 CP
Mrs. Mongold
Steps to Solve Multi-Step
Equations
Steps to Solve Multi-Step
Equations
• 1. Combine like terms on each side of the
equation
Steps to Solve Multi-Step
Equations
• 1. Combine like terms on each side of the
equation
• 2. Isolate the variable… equation should have
the variable on one side and a constant on the
other
Steps to Solve Multi-Step
Equations
• 1. Combine like terms on each side of the
equation
• 2. Isolate the variable… equation should have
the variable on one side and a constant on the
other
• 3. Get the variable by itself completely, remove
all coefficients.
Steps to Solve Multi-Step
Equations
• 1. Combine like terms on each side of the
equation
• 2. Isolate the variable… equation should have
the variable on one side and a constant on the
other
• 3. Get the variable by itself completely, remove
all coefficients.
• 4. CHECK your answer in the original
problem…. EVERY TIME… this is not an option
it’s a requirement
Examples:
Examples:
Examples:
Examples:
Examples:
Examples:
𝑝 = −39
Examples:
Examples:
Examples:
Examples:
Examples:
Examples:
Examples:
Examples:
Examples:
2
CHECK 3 210 − 25 = 115
140 – 25 = 115
Word Problems and Problem
Solving
• Consecutive numbers
Word Problems and Problem
Solving
• Consecutive numbers are numbers that go in
numerical order, counting by 1
Word Problems and Problem
Solving
• Consecutive numbers are numbers that go in
numerical order, counting by 1
– Example: 1, 2, 3
and -10, -9, -8
Word Problems and Problem
Solving
• Consecutive numbers are numbers that go in
numerical order, counting by 1
– Example: 1, 2, 3
and -10, -9, -8
Represent these algebraically in terms of x
Word Problems and Problem
Solving
• Consecutive numbers are numbers that go in
numerical order, counting by 1
– Example: 1, 2, 3
and -10, -9, -8
Represent these algebraically in terms of x
x, x +1, x + 2, x + 3, x + 4, ….
Word Problems and Problem
Solving
• Consecutive Even Numbers:
Word Problems and Problem
Solving
• Consecutive Even Numbers: numbers in
numerical order that are divisible by 2 evenly
Word Problems and Problem
Solving
• Consecutive Even Numbers: numbers in
numerical order that are divisible by 2 evenly
– Example: 2, 4, 6
and -6, -4, -2
Word Problems and Problem
Solving
• Consecutive Even Numbers: numbers in
numerical order that are divisible by 2 evenly
– Example: 2, 4, 6
and -6, -4, -2
To represent these algebraically in term of x
Word Problems and Problem
Solving
• Consecutive Even Numbers: numbers in
numerical order that are divisible by 2 evenly
– Example: 2, 4, 6
and -6, -4, -2
To represent these algebraically in term of x
x, x + 2, x + 4, x + 6, …
Word Problems and Problem
Solving
• Consecutive Odd Numbers:
Word Problems and Problem
Solving
• Consecutive Odd Numbers: numbers in
numerical order that are not divisible by 2
Word Problems and Problem
Solving
• Consecutive Odd Numbers: numbers in
numerical order that are not divisible by 2
– Example: 3, 5, 7
and
-9, -7, -5
Word Problems and Problem
Solving
• Consecutive Odd Numbers: numbers in
numerical order that are not divisible by 2
– Example: 3, 5, 7
and
-9, -7, -5
Represent these algebraically in terms of x
Word Problems and Problem
Solving
• Consecutive Odd Numbers: numbers in
numerical order that are not divisible by 2
– Example: 3, 5, 7
and
-9, -7, -5
Represent these algebraically in terms of x
x, x + 2, x + 4, x + 6, …
When doing word problems…
•
•
•
•
1. Define your variables
2. Write your equation
3. Solve your equation
4. Plug your answers back in to get ALL of
the numbers in the problem not just x
Find three consecutive integers whose
sum is 21
Find three consecutive integers whose
sum is 21
• Define variable:
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Solve:
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Solve: 3x + 3 = 21
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Solve: 3x + 3 = 21
-3
-3
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Solve: 3x + 3 = 21
-3
-3
3x = 18
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Solve: 3x + 3 = 21
-3
-3
3x = 18
3
3
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Solve: 3x + 3 = 21
-3
-3
3x = 18
3
3
x=6
Find three consecutive integers whose
sum is 21
• Define variable: x = first of three numbers
• Write an equation:
x + (x +1) + (x + 2) = 21
Solve: 3x + 3 = 21
PLUG BACK IN to answer
-3
-3
the question!!
3x = 18
The three numbers are 6,
7, and 8
3
3
CHECK 6 + 7 + 8 = 21
x=6
Find three consecutive even
integers whose sum is -42
Find three consecutive even
integers whose sum is -42
• Define variable:
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
x + (x + 2) + (x + 4) = -42
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
x + (x + 2) + (x + 4) = -42
• Solve: 3x + 6 = -42
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
x + (x + 2) + (x + 4) = -42
• Solve: 3x + 6 = -42
-6
-6
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
x + (x + 2) + (x + 4) = -42
• Solve: 3x + 6 = -42
-6
-6
3x = -48
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
x + (x + 2) + (x + 4) = -42
• Solve: 3x + 6 = -42
-6
-6
3x = -48
3
3
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
x + (x + 2) + (x + 4) = -42
• Solve: 3x + 6 = -42
-6
-6
3x = -48
3
3
x = -16
Find three consecutive even
integers whose sum is -42
• Define variable: x = first of the even
numbers
• Write an equation:
x + (x + 2) + (x + 4) = -42
• Solve: 3x + 6 = -42 PLUG BACK IN to answer
question
three even integers are
-6
-6 The
-16, -14, -12
3x = -48
3
3 CHECK -16 + (-14) + (-12) = -42
x = -16