Which of the equations shown have infinitely many solutions? Select all that apply. А. Зх-13 3x +1 В. 2х -1%3D1- 2х п С. Зх — 2 %3D 2х-3 D. 3(x- 1) %3D 3х- 3 Е 2x + 2 %3D 2(х + 1) F. 3(x- 2) %3D2(х - 3)
Which of the equations shown have infinitely many solutions? Select all that apply. А. Зх-13 3x +1 В. 2х -1%3D1- 2х п С. Зх — 2 %3D 2х-3 D. 3(x- 1) %3D 3х- 3 Е 2x + 2 %3D 2(х + 1) F. 3(x- 2) %3D2(х - 3)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
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Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Which of the equations shown have infinitely many solutions? Select all that apply.**
- [ ] **A.** \( 3x - 1 = 3x + 1 \)
- [ ] **B.** \( 2x - 1 = 1 - 2x \)
- [ ] **C.** \( 3x - 2 = 2x - 3 \)
- [ ] **D.** \( 3(x - 1) = 3x - 3 \)
- [ ] **E.** \( 2x + 2 = 2(x + 1) \)
- [ ] **F.** \( 3(x - 2) = 2(x - 3) \)
**Explanation:**
This is a multiple-choice question asking which equations out of the given six have infinitely many solutions. To determine this, each equation must be analyzed to see if it simplifies to a true statement (i.e., be an identity).
-A) \( 3x - 1 = 3x + 1 \): Simplifies to \( -1 = 1 \) which is false, hence no solutions.
-B) \( 2x - 1 = 1 - 2x \): Simplifies to \( 4x = 2 \), so \( x = \frac{1}{2} \), hence one solution only.
-C) \( 3x - 2 = 2x - 3 \): Simplifies to \( x = -1 \), hence one solution only.
-D) \( 3(x - 1) = 3x - 3 \): Simplifies to \( 3x - 3 = 3x - 3 \), which is true for all \( x \), hence infinitely many solutions.
-E) \( 2x + 2 = 2(x + 1) \): Simplifies to \( 2x + 2 = 2x + 2 \), which is true for all \( x \), hence infinitely many solutions.
-F) \( 3(x - 2) = 2(x - 3) \): Simplifies to \( 3x - 6 = 2x - 6 \), so \( x = 0 \), hence one solution only.
Thus, options D and E have infinitely many solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F134eae91-dd6f-48be-900f-3863236bf515%2F7d8ec0c4-6353-4378-9d72-dc04dabd22a2%2Fzhqvs5b_processed.png&w=3840&q=75)
Transcribed Image Text:**Which of the equations shown have infinitely many solutions? Select all that apply.**
- [ ] **A.** \( 3x - 1 = 3x + 1 \)
- [ ] **B.** \( 2x - 1 = 1 - 2x \)
- [ ] **C.** \( 3x - 2 = 2x - 3 \)
- [ ] **D.** \( 3(x - 1) = 3x - 3 \)
- [ ] **E.** \( 2x + 2 = 2(x + 1) \)
- [ ] **F.** \( 3(x - 2) = 2(x - 3) \)
**Explanation:**
This is a multiple-choice question asking which equations out of the given six have infinitely many solutions. To determine this, each equation must be analyzed to see if it simplifies to a true statement (i.e., be an identity).
-A) \( 3x - 1 = 3x + 1 \): Simplifies to \( -1 = 1 \) which is false, hence no solutions.
-B) \( 2x - 1 = 1 - 2x \): Simplifies to \( 4x = 2 \), so \( x = \frac{1}{2} \), hence one solution only.
-C) \( 3x - 2 = 2x - 3 \): Simplifies to \( x = -1 \), hence one solution only.
-D) \( 3(x - 1) = 3x - 3 \): Simplifies to \( 3x - 3 = 3x - 3 \), which is true for all \( x \), hence infinitely many solutions.
-E) \( 2x + 2 = 2(x + 1) \): Simplifies to \( 2x + 2 = 2x + 2 \), which is true for all \( x \), hence infinitely many solutions.
-F) \( 3(x - 2) = 2(x - 3) \): Simplifies to \( 3x - 6 = 2x - 6 \), so \( x = 0 \), hence one solution only.
Thus, options D and E have infinitely many solutions.
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