Multistep Equations
How to Identify Multistep Equations
• Some equations can be solved in one or two steps
• Ex) 4x + 2 = 10 is a two-step equation
• Subtract 2
• Divide both sides by 4
• Multistep equation – an equation whose solution
requires more than two steps
• Ex) 5x – 4 = 3x + 2 and 4(x – 2) = 12
• Multistep equations can take different forms
• Variables present in two different terms
Characteristic
Multiple variable or
constant terms on the
same side
Variable present on both
sides
Parentheses present on
either side
Example
x + 2x + 3x – 1 = 3 + 20
4x – 2 = 3x + 3
3(x + 2) = 21
Combining Terms
• First step to solving a multistep equation is to simplify each side
• Use the distributive property to eliminate parentheses
• Ex) 5(x – 2) + x = 2(x + 3) simplifies to 5x – 10 + x = 2x + 6 + 4
• Combine like terms
• Ex) 5x – 10 + x = 2x + 6 + 4 simplifies to 6x – 10 = 2x + 10
• Terms containing variables cannot be combined with terms
How to Solve Multistep Equations
• Consider the equation 4(x + 2) – 10 = 2(x + 4)
• Simplify with the distributive property
• Combine like terms
• Eliminate the unknown from one side
• Eliminate the constant term on the other side
• Divide each side by the coefficient of the variable
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Algebra I 2.7 – Multistep Equations
Multistep Equations
Consecutive Integers
• Consecutive integers – integers that are separated by exactly one unit
• Set of consecutive integers from –1 to 3
• When domain is limited to integers, the letter n is used to represent the variable
• Ex) Find 3 consecutive integers that have a sum of 24
• Solution is 7, 8, 9
• Consecutive even integers are spaced two units apart
• Consecutive odd integers are spaced two units apart, as well
Multistep Inequalities
• Multistep inequalities can be solved in the same way as multistep equations
• Ex) 2x + 12 ≤ 6x can be made into a two-step inequality
• Subtract 2x from each side to produce 12 ≤ 4x
• Divide by 4 to yield 3 ≤ x
• Placing the variable on the left requires the inequality sign to be flipped, x ≥ 3
• Numbers in the solution range, such as 5, can illustrate that the statements x ≥ 3 and –x ≤ –3 are
equivalent
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Algebra I 2.7 – Multistep Equations