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First-Degree Equations

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Questions and Answers

What is the general form of a first-degree equation?

ax + b = 0 (correct)

ax + by = c

a/x + b = c

ax^2 + bx + c = 0

What is the solution to the equation 2x - 5 = 3x + 1?

x = 2

x = -6

x = -2 (correct)

x = 6

Which of the following is a valid step in solving the equation 4(x + 3) = 2x - 5?

Combine like terms first and then distribute 4

Distribute 4 and then combine like terms (correct)

Combine like terms first and then add 3 to both sides

Distribute 4 and then add 3 to both sides

What is the first step in solving the equation 3x - 7 = 2x + 5?

Add 7 to both sides Signup and view all the answers

What is the solution to the equation 2(3x - 4) = 5x + 6?

x = 2 Signup and view all the answers

Which of the following is a valid step in solving the equation 4x - 8 = 2(3x + 1)?

Distribute the 2 on the right side Signup and view all the answers

Study Notes

First-Degree Equations

A first-degree equation, also known as a linear equation, is represented in the form Ax + B = C, where A, B, and C are constants and x is the variable.

Solution to Specific Equations

The solution to the equation 2x - 5 = 3x + 1 is found by isolating x, resulting in x = -6.
For the equation 3x - 7 = 2x + 5, the first step is typically to rearrange it to isolate x, usually by subtracting 2x from both sides, yielding x - 7 = 5.

Valid Steps in Solving Equations

In solving the equation 4(x + 3) = 2x - 5, distributing the 4 on the left side is a valid first step.
In the equation 4x - 8 = 2(3x + 1), a valid step includes distributing 2 on the right side, transforming it to 4x - 8 = 6x + 2.

Additional Solutions

The equation 2(3x - 4) = 5x + 6 simplifies by distributing 2, leading to 6x - 8 = 5x + 6, which can be solved to find x = 14.

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Description

Test your knowledge of first-degree equations with this quiz. Explore the general form of these equations and solve problems involving linear equations. Practice solving equations step by step and enhance your understanding of this fundamental algebraic concept.