Solve for x.

Question

3x + 2=x+8

A. 1.5

B. 2.5

• с.3

• D.5

Answer 1

To solve the equation \(3x + 2 = x + 8\), follow these steps:

1. Subtract \(x\) from both sides:

\[ 3x - x + 2 = 8 \]

This simplifies to:

\[ 2x + 2 = 8 \]

2. Next, subtract 2 from both sides:

\[ 2x = 8 - 2 \]

This simplifies to:

\[ 2x = 6 \]

3. Finally, divide both sides by 2:

\[ x = \frac{6}{2} = 3 \]

So the solution is:

\[ x = 3 \]

The correct answer is C. 3.

Answer 2

Which equations have infinitely many solutions? Select TWO that apply.
A. 6(x-9) = 6x -54+x
B. 5(x - 8) + 10 = 5(x + 2)
C. 20 - 8x-6 = 2(7 - 4x)
D. 4(x+4) = 2(2x+5) + 6
E. 2x + 9 = 18 + 2x

Answer 3

To determine which equations have infinitely many solutions, we need to simplify each equation and see if they result in a true statement (like \(0 = 0\)) or a false statement (like \(0 = 5\)). Equations that are the same on both sides will have infinitely many solutions. Let's analyze each option.

A. \(6(x-9) = 6x - 54 + x\)

Distributing on the left side:

\[ 6x - 54 = 6x - 54 + x \]

Simplifying the right side:

\[ 6x - 54 = 7x - 54 \]

Subtract \(6x\) from both sides:

\[ -54 = x - 54 \]

Add \(54\) to both sides:

\[ 0 = x \]

This has one solution (\(x = 0\)), not infinitely many.

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B. \(5(x - 8) + 10 = 5(x + 2)\)

Distributing on the left side:

\[ 5x - 40 + 10 = 5x + 10 \]

This simplifies to:

\[ 5x - 30 = 5x + 10 \]

Subtract \(5x\) from both sides:

\[ -30 = 10 \]

This is a false statement, so it has no solutions.

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C. \(20 - 8x - 6 = 2(7 - 4x)\)

Simplifying the left side:

\[ 14 - 8x = 14 - 8x \]

Both sides are identical, indicating this equation has infinitely many solutions.

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D. \(4(x+4) = 2(2x+5) + 6\)

Distributing:

\[ 4x + 16 = 4x + 10 + 6 \]

Simplifying the right side:

\[ 4x + 16 = 4x + 16 \]

Again, both sides are identical, indicating this equation also has infinitely many solutions.

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E. \(2x + 9 = 18 + 2x\)

Subtracting \(2x\) from both sides gives:

\[ 9 = 18 \]

This is a false statement, so it has no solutions.

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Summary:

The equations with infinitely many solutions are:

• C. \(20 - 8x - 6 = 2(7 - 4x)\)
• D. \(4(x+4) = 2(2x+5) + 6\)

So the correct answers are C and D.