Questions: Pre-Calculus Algebra- SMAT 121S- 003- Fall 2024 (12104) Angela Netter 1.1 Linear Equations Question 5, 1.1.VQ-3 4 correct Part 1 of 2 Points: 0 of 1 Question list Question 1 Question 2 Question 3 Question 4 Watch the video and then solve the problem given below. Find the solution set. Then indicate whether the equation is conditional, an identity, or 21(x-1)=-7(3-x)+14 x Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is □ B. The solution is the set of all real numbers. C. The solution is the empty set.

Solution Steps

To solve the given linear equation, we need to simplify both sides of the equation and then solve for \( x \). We will then determine if the equation is conditional (has a specific solution), an identity (true for all values of \( x \)), or has no solution (empty set).

1. Distribute the constants on both sides of the equation.
2. Combine like terms.
3. Isolate \( x \) to find its value.
4. Determine the nature of the solution set.

First, we need to distribute the constants on both sides of the equation: \[ 21(x - 1) = -7(3 - x) + 14x \]

Distribute the constants: \[ 21x - 21 = -21 + 7x + 14x \]

Combine like terms on the right side: \[ 21x - 21 = -21 + 21x \]

Subtract \(21x\) from both sides to isolate the constants: \[ 21x - 21 - 21x = -21 + 21x - 21x \]

This simplifies to: \[ -21 = -21 \]

Since the equation simplifies to \(-21 = -21\), which is always true, the equation is an identity. This means that the solution set is all real numbers.

Final Answer