18 Questions
What is the first step in solving a linear equation?
Apply the distributive property
Which property states that multiplying each term in an expression by the same quantity does not change the equality of the expressions?
Distributive property
What is the purpose of combining like terms in algebraic equations?
To simplify the equation by adding or subtracting coefficients
When solving a linear equation, what does it mean if the variable is in 'standard form'?
Variable is on one side and constants on the other
In the equation $3(x + 2) = 9$, what should be done first to solve for $x$?
Distribute $3$ into $(x + 2)$
If given $5x + 3 = -7$, what is the correct first step to solve for $x$?
Add 3 to both sides
What is the first step in solving a linear equation with one variable on both sides?
Combine like terms
What is the next step after combining like terms when solving a linear equation?
Isolate the variable term
Which property allows us to multiply a sum by a constant?
Distributive Property
In solving a linear equation, what does dividing by the coefficient of the variable term help to achieve?
Isolate the variable
What is the primary purpose of checking a solution after solving a linear equation?
Check if the solution satisfies the original equation
In the equation $4x - 3 = 2 - 2x$, what is the first step to solve for $x$?
Combine like terms
When solving a linear equation, why is it important to apply the distributive property?
To isolate the variable term
When solving a linear equation, what is the purpose of combining like terms?
To rearrange the equation
What should be done if a solution to a linear equation does not satisfy the original equation upon checking?
Re-evaluate the steps used for combining like terms
What is the next step after combining like terms in a linear equation with one variable on both sides?
Isolate the variable
In solving linear equations with one variable on both sides, what is necessary to do before checking the solution?
Isolate the variable on one side
What technique is essential for solving linear equations with one variable on both sides?
Combining like terms
Study Notes
Solving Linear Equations
Linear equations are fundamental building blocks in algebra. They typically feature one variable, often represented by a letter like (x), and are written in the form (ax + b = 0), where (a) and (b) are constants. Solving these equations means finding the value of the variable that satisfies the equation.
The Distributive Property
The distributive property is a cornerstone in solving linear equations. It states that multiplying each term in an expression by the same quantity does not change the equality of the expressions. In other words, (a(x + b) = ax + ab).
Combining Like Terms
Before solving for a variable, it's often necessary to combine like terms. Like terms are variables (such as (x)) or constants that are raised to the same power and multiplied by the same coefficients. For example, (4x) and (7x) are like terms, as are (x^2) and (3x^2). Combining like terms means adding or subtracting their coefficients.
Solving for Variables
Once like terms have been combined, solving for a variable involves isolating the variable. When the variable is on one side of the equation and all constants are on the other, the variable is said to be in "standard form." The general rule is to apply inverse operations to eliminate the variable from one side of the equation, leaving it on the other side.
For example, consider the linear equation (2x + 5 = 11). To solve for (x), first subtract (5) from both sides: (2x + 5 - 5 = 11 - 5). This simplifies to (2x = 6). Next, divide both sides by (2): (\frac{2x}{2} = \frac{6}{2}). This simplifies to (x = 3).
Solving Equations of Different Forms
Not all linear equations are in the form (ax + b = 0). For instance, (3x - 4 = 7) is an example of a linear equation in the form (ax + b = c). To solve this type of equation, follow the same steps as in the previous example, but keep in mind that the solution is the value of the variable that makes the equation true.
Keep in mind that solving linear equations is a foundational skill, and understanding these concepts will help you tackle more complex problems in algebra and beyond.
Master the fundamentals of solving linear equations with this quiz. Learn about the distributive property, combining like terms, and isolating variables to find their values. Enhance your algebra skills by understanding the steps involved in solving linear equations of different forms.
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