Equations
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Contents
 Solving Equations
 OneStep Equation
 TwoStep Equation
 MultiStep Equation with Variable on One Side
 MultiStep Equation with Variables on Both Sides
 Word Problems
 Distance Rate Time
Solving Equations
Equations containing one or more variables are algebra equations. Variables represent unknown amounts, and any letter or symbol can be used as a variable.
Algebra equations may need onestep, twosteps, or multiplesteps to solve for the value of the variable. Equations may have variables on one or both sides of the equal sign. To solve algebra equations, students combine like terms and use inverse operations to isolate the variable. Equations in the format of variable word problems may help students learn to apply algebra skills to real world situations.
OneStep Equation
To isolate the variable to solve these onestep equations, undo the equation:
Example 1: Undo the constant by subtracting from both sides of the equation.
$\begin{array}{lcl} x + 3 & = & 8 \\ x + 3  3 & = & 8  3 \\ x & = & 5 \end{array}$
Example 2: Divide both sides of the equation by the coefficient.
$\begin{array}{lcl} 2x & = & 16\\ \frac{2}{2}x & = & \frac{16}{2} \\ x& = &8 \end{array}$
TwoStep Equation
Use reverse PEMDAS to solve this twostep equation.
Step 1: Subtract the constant from both sides of the equation.
Step 2: Divide both sides of the equation by the coefficient.
$\begin{array}{lcl} 3x + 5 &= & 17 \\ 3x + 5 5 &= &17 5\\ 3x&=&12 \\ \frac{3}{3}x&=&\frac{12}{3} \\ x&=&4 \end{array}$
MultiStep Equation with Variable on One Side
Use the Distributive Property to solve this multistep equation:
Step 1: Apply the Distributive Property.
Step 2: Add the constant to both sides of the equation.
Step 3: Divide both sides of the equation by the coefficient.
$\begin{array}{lcl} 8 &= &2(x  2)\\ 8&=&2x 4 \\ 8 +4&=&2x 4 +4 \\ 12&=&2x \\ \frac{12}{2}&=&\frac{2}{2}x \\ x&=&6 \end{array}$
MultiStep Equation with Variables on Both Sides
To solve multistep equations such as this, combine like terms to make the problem easier to solve:
Step 1: Use opposite operations to combine like terms.
Step 2: Divide both sides of the equation by the coefficient.
$\begin{array}{lcl} 11x&=& 16 + 3x\\ 11x  3x &=& 16 + 3x 3x \\ 8x &=& 16 \\ \frac{8}{8}x&=&\frac{16}{8}\\ x&=& 2 \end{array}$
Word Problems
Write a variable equation to solve this word problem. Let x represent the number of people attending the party.
Husni bakes cakes for a party. He doesn’t know how many people will attend, but he does know he needs 3 eggs per cake and a cake serves 8 people. Write an expression to determine the number of eggs he will need.
$(\frac{x}{8})\times3$
If 24 people attend the party, how many eggs will he need?
$(\frac{24}{8})\times3 = 3\times3=9$
He needs 9 eggs.
Distance Rate Time
Use the Distance Rate Time (DRT) formula to solve problems of how far, how long, or how fast. Using the formula, calculate problems for travel in the same direction or different directions. The following triangles will help you to remember:
Distance Rate Time – Same Direction
Example 1: Use the DRT formula to solve this problem: Alex rode his bike for 2 hours travelling 23 miles. What is his rate?
D = 23 miles
T = 2 hours
R = x
$\begin{array}{lcl} 23&=&2x\\ x&=&11.5 \end{array}$
Alex’s rate is 11.5 miles per hour.
Example 2: After school, Kara and Cyrus ride bikes with the riding club. Kara leaves school at 3:00 pm, riding 10 miles per hour. Cyrus stayed a few minutes late to clean out his locker and left at 3:10 pm, riding at a rate of 12 miles per hour. When will he catch up with Kara?
$\begin{array}{lcl} 10t &=& 12(t\frac{1}{6}) \\ 10t&=&12t 2 \\ 10t 12t&=&12t 12t 2 \\ 2t&=&2 \\ \frac{2}{2}t&=&\frac{2}{2} \\ 2t&=&2 \\ t&=&1 \end{array}$
After one hour, Cyrus will catch up with Kara.
Distance Rate Time – Different Directions
For this problem, the travel is from two different directions. Use the DRT formula to solve: Carly and Pete leave school traveling in opposite directions on a straight road. Pete rides his electric bike 12 mi/h faster than Carly walks. After 2 hours, they are 36 miles apart. Find Carly’s rate and Pete’s rate.
$\begin{array}{lcl} 2(12+x) + 2x &=&36\\ 24 +2x +2x&=&36\\ 24 +4x&=&36\\ 24 24 +4x&=&36 24\\ 4x&=&12\\ \frac{4}{4}x&=&\frac{12}{4} \\ x&=&3 \end{array}$
Carly’s rate is 3 mph, and Pete’s rate is 15.
All Videos in this Topic
Videos in this Topic
Equations (7 Videos)
All Worksheets in this Topic
Worksheets in this Topic
Equations (7 Worksheets)

Solving OneStep Equations
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Solving TwoStep Equations
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Solving MultiStep Equations with Variables on One Side
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Solving MultiStep Equations with Variables on Both Sides
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Solving Equations: Word Problems
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Distance  Rate  Time – Same Direction
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Distance  Rate  Time – Different Directions
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