EQ - Solve Multi-Step Equations Lesson

Solve Multi-Step Equations

image of key In this lesson, you will learn to solve multistep equations. The goal is to transform each equation into a two-step equation, which you already know how to solve. Think of solving a puzzle. The key to this puzzle is to identify how to undo all of the operations to unlock the solution!

You will use what you have learned about combining like terms and the distributive property to solve multistep equations. Let's look at an example of these types of equations.

Example 1: Combining like terms to solve equations.

$LaTeX: 6n-1-3n=17\\ 3n-1=17 \textcolor{green}{\:\text{Combine like terms 6n-3n and simplify.}}\\ \:\:\:+1\:\:\:+1\:\textcolor{green}{\text{Add 1 to both sides.}}\\ \frac{3n}{3}=\frac{18}{3}\:\textcolor{green}{\text{Divide both sides by 3.}}\\ n=6$ $6n-1-3n=17\\ 3n-1=17 \textcolor{green}{\:\text{Combine like terms 6n-3n and simplify.}}\\ \:\:\:+1\:\:\:+1\:\textcolor{green}{\text{Add 1 to both sides.}}\\ \frac{3n}{3}=\frac{18}{3}\:\textcolor{green}{\text{Divide both sides by 3.}}\\ n=6$

Check your solution: 6(6) - 1 - 3(6) = 17; 36 - 1 - 18 = 17; 35 - 18 = 17

Example 2: Using the Distributive Property to solve equations.

$LaTeX: 2\left(z+5\right)+4=-12 \\ 2z+10+4=-12\:\textcolor{green}{\text{Use the Distributive Property to clear the parenthesis.}}\\ 2z+14=-12\:\textcolor{green}{\text{Combine like terms.}}\\ \:\:\:\textcolor{green}{-14\:\:\:-14\:\:\text{Subtract 14 from both sides.}}\\ \frac{2z}{2}=-\frac{26}{2}\textcolor{green}{\:\text{Divide both sides by 2.}}\\ z=-13$ $2\left(z+5\right)+4=-12 \\ 2z+10+4=-12\:\textcolor{green}{\text{Use the Distributive Property to clear the parenthesis.}}\\ 2z+14=-12\:\textcolor{green}{\text{Combine like terms.}}\\ \:\:\:\textcolor{green}{-14\:\:\:-14\:\:\text{Subtract 14 from both sides.}}\\ \frac{2z}{2}=-\frac{26}{2}\textcolor{green}{\:\text{Divide both sides by 2.}}\\ z=-13$

Check your solution: 2 (-13 + 5) + 4 = -12; 2(-8) + 4 = -12; -16 = 4 = -12

Investigate

image of baseball card Rae owns three times as many baseball cards as Haley. Subtracting 9 from the number of baseball cards Rae owns and then dividing by 6 gives the number of cards Steve owns. If Steve owns 24 baseball cards, how many baseball cards does Haley own?

Strategy

Summarize the problem, using only key words or phrases and rewrite the problem as a statement.

Find the number of baseball cards that Haley owns. (Let h represent Haley's cards)

Rae owns 3 times as many as Haley. (3h)

Subtracting 9 from the number of cards Rae owns and then dividing by 6 is Steve's cards. $LaTeX: \frac{Rae-9}{6}$ $\frac{Rae-9}{6}$

Steve owns 24 cards.

Now, translate this information into a multistep equation and solve.

$LaTeX: \frac{3h-9}{6}=24\\ (6)\frac{3h-9}{6}=24(6)\:\:\textcolor{green}{\text{Multiply both sides by 6.}}\\ 3h-9=144\\ \:\:\:+9\:\:\:+9\:\:\textcolor{green}{\text{Add 9 to both sides}}\\ 3h=153\\ \frac{3h}{3}=\frac{153}{3}\:\textcolor{green}{\text{Divide both sides by 3.}}\\ h=51$ $\frac{3h-9}{6}=24\\ (6)\frac{3h-9}{6}=24(6)\:\:\textcolor{green}{\text{Multiply both sides by 6.}}\\ 3h-9=144\\ \:\:\:+9\:\:\:+9\:\:\textcolor{green}{\text{Add 9 to both sides}}\\ 3h=153\\ \frac{3h}{3}=\frac{153}{3}\:\textcolor{green}{\text{Divide both sides by 3.}}\\ h=51$

Interpret the solution: Haley owns 51 baseball cards.

Take a moment to practice solving these equations here!

Solving Multi-Step Equations Practice

Solve Multi-Step Equations Homework

Now that you have spent some time learning strategies for solving multi-step equations, you are ready to complete your Equations: Solving Multi-step Equations Homework. Download your homework by CLICKING HERE. Links to an external site.

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key Links to an external site..

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