Topics
6. Equations & Inequalities
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United States of America
Grade 7

Review: One-step equations

Lesson
Practice

Keep equations balanced

We want to keep equations balanced so that the two sides of the equals sign remain equivalent. If we don't we could change what the equation means. Think of a balanced set of scales. The scale remains level when the weights on both side of the scales are even. The same thing happens with equations.

An image showing two balanced scales with tiles on it. Ask your teacher for more information.

If we add a weight to one side and not to the other, then the scales will no longer be balanced. Keep equations balanced by always performing the exact same operation to both sides of the equation.

Exploration

This applet represents the equation x = 5. What equivalent equations can we make by doing the same thing to both sides? See if we can come up with 4 different equations.

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Changing the weights on both sides of the balance will change the equation accordingly. In the same way, changing only one side of an equation will make it unbalanced.

Examples

Example 1

Beginning with the equation x=14, write the new equation produced by subtracting 7 from both sides.

Worked Solution
Create a strategy

Perform the given operation to both sides of the equation.

Apply the idea
\displaystyle x -7\displaystyle =\displaystyle 14-7Substract 11 from both sides
\displaystyle x-7\displaystyle =\displaystyle 7Evaluate

Example 2

Beginning with the equation x=99, write the new equation produced by dividing both sides by 11.

Worked Solution
Create a strategy

Perform the given operation to both sides of the equation.

Apply the idea
\displaystyle x \div 11\displaystyle =\displaystyle 99 \div 11Divide both sides by 11
\displaystyle \frac{x}{11}\displaystyle =\displaystyle 9Evaluate and simplify
Idea summary

Keep equations balanced by always performing the exact same operation to both sides of the equation.

Solve a one-step equation

We can often solve for an unknown value by writing an equation and then solving for the unknown value, often represented with a variable.

To solve for the unknown variable:

  • We want to get the variable by itself on one side of the equals sign.
  • We must do the same operations to both sides equation to keep it balanced.
  • We should use inverse operations to solve such as addition and subtraction, and multiplication and division.

Examples

Example 3

Solve: x+6=15

Worked Solution
Create a strategy

Use the fact that subtraction is the opposite of addition.

Apply the idea
\displaystyle x+6 -6\displaystyle =\displaystyle 15-6Subtract 6 from both sides
\displaystyle x\displaystyle =\displaystyle 9Evaluate

Example 4

Find the value of x where: 3x=18

Worked Solution
Create a strategy

Use the fact that division is the opposite of multiplication.

Apply the idea
\displaystyle \dfrac{3x}{3} \displaystyle =\displaystyle \dfrac{18}{3}Divide both sides by 3
\displaystyle x\displaystyle =\displaystyle 6Evaluate

Example 5

Solve: \dfrac{x}{-10}=-9

Worked Solution
Create a strategy

Use the fact that multiplication is the opposite of division.

Apply the idea
\displaystyle \frac{x}{-10} \times -10\displaystyle =\displaystyle -9 \times -10Multiply -10 to both sides
\displaystyle x\displaystyle =\displaystyle 90Evaluate
Idea summary

To solve one-step equations:

  • We want to get the variable by itself on one side of the equals sign
  • We must do the same operations to both sides of the equation to keep it balanced
  • We should use inverse operations such as addition and subtraction, and multiplication and division

Outcomes

7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.EE.B.4.A

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

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