Equation Solving Examples

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Questions and Answers

What is the value of $x$ in Equation 1?

$rac{8}{3}$
$rac{56}{45}$ (correct)
$rac{28}{45}$
$rac{7}{9}$

What is $x$ in Equation 2?

$rac{27}{35}$ (correct)
$rac{14}{15}$
$rac{9}{5}$
$rac{3}{7}$

Which equation directly solves for $x = 2 rac{1}{3}$?

Equation 5
Equation 4
Equation 3 (correct)
Equation 1

In Equation 5, what is the final result for $x$?

<p>$rac{48}{77}$ (A)</p> Signup and view all the answers

What operation must be applied to isolate $x$ in Equation 4?

<p>Multiply both sides by $rac{9}{7}$ (D)</p> Signup and view all the answers

Flashcards

Solving for a Variable

To solve for a variable in an equation, you must isolate the variable on one side of the equation. This can be achieved by performing the same operations on both sides of the equation.

Reciprocal Property

When a fraction is multiplied by its reciprocal, the product equals 1. This is a helpful property for solving equations where the variable is multiplied by a fraction.

Mixed Numbers & Improper Fractions

A mixed number combines a whole number and a fraction. To solve equations with mixed numbers, it's often easier to convert them into improper fractions.

Inverse Operations

To solve for a variable in an equation, you must perform the opposite operation of what's being done to the variable. For example, if the variable is being multiplied, you must divide to isolate it.

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Multiplication of Fractions

Multiplying fractions involves multiplying the numerators and the denominators of the fractions. Simplifying fractions helps to make the calculations easier.

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