Solve the following equation for xx. Express your answer in the simplest form.

To solve the equation \( 5(-4x + 5) = 4(-5x + 6) \), we will first distribute on both sides.

Starting with the left side: \[ 5(-4x + 5) = 5 \cdot -4x + 5 \cdot 5 = -20x + 25 \]

Now, for the right side: \[ 4(-5x + 6) = 4 \cdot -5x + 4 \cdot 6 = -20x + 24 \]

Now we rewrite the equation with the distributed values: \[ -20x + 25 = -20x + 24 \]

Next, we will try to isolate the variable. To do this, let's add \( 20x \) to both sides: \[ -20x + 20x + 25 = -20x + 20x + 24 \] This simplifies to: \[ 25 = 24 \]

Since 25 does not equal 24, this result indicates that there is no solution to the equation.

Thus, the answer is: A: no solution.

Solve the following equation for xx. Express your answer in the simplest form.
minus, 8, left parenthesis, minus, 3, x, minus, 2, right parenthesis, equals, 24, x, plus, 15
−8(−3x−2)=
24x+15

A: no solution
B:infinitely many solutions
C:one solution

To solve the equation \( -8(-3x - 2) = 24x + 15 \), we begin by distributing the \(-8\) on the left side.

Starting with the left side: \[ -8(-3x - 2) = 8 \cdot 3x + 8 \cdot 2 = 24x + 16 \]

So, we rewrite the equation: \[ 24x + 16 = 24x + 15 \]

Next, we will try to isolate the variable by subtracting \(24x\) from both sides: \[ 24x + 16 - 24x = 24x + 15 - 24x \] This simplifies to: \[ 16 = 15 \]

Since 16 does not equal 15, this result indicates that there is no solution to the equation.

Thus, the answer is: A: no solution.

Solve the following equation for xx. Express your answer in the simplest form.
5, left parenthesis, minus, 2, x, minus, 3, right parenthesis, equals, 9, x, plus, 21
5(−2x−3)=
9x+21

A: no solution
B:infinitely many solutions
C:one solution

To solve the equation \( 5(-2x - 3) = 9x + 21 \), we first distribute on the left side.

Starting with the left side: \[ 5(-2x - 3) = 5 \cdot -2x + 5 \cdot -3 = -10x - 15 \]

Now we rewrite the equation: \[ -10x - 15 = 9x + 21 \]

Next, we will isolate the variable \( x \). We can do this by adding \( 10x \) to both sides: \[ -10x + 10x - 15 = 9x + 10x + 21 \] This simplifies to: \[ -15 = 19x + 21 \]

Next, we will subtract \( 21 \) from both sides: \[ -15 - 21 = 19x + 21 - 21 \] This simplifies to: \[ -36 = 19x \]

Now, we divide both sides by \( 19 \) to solve for \( x \): \[ x = \frac{-36}{19} \]

Thus, the solution in simplest form is: \[ x = -\frac{36}{19} \]

Since we found a specific value for \( x \), the answer is: C: one solution.

What’s the 1 solution?

The one solution for the equation \( 5(-2x - 3) = 9x + 21 \) is:

\[ x = -\frac{36}{19} \]

This is the value of \( x \) that satisfies the equation.

Solve the following equation for xx. Express your answer in the simplest form.
minus, left parenthesis, 2, x, plus, 8, right parenthesis, equals, minus, 3, left parenthesis, minus, x, plus, 1, right parenthesis
−(2x+8)=
−3(−x+1)

A: no solution
B:infinitely many solutions
C:one solution

To solve the equation

\[ -(2x + 8) = -3(-x + 1) \]

we'll first simplify both sides.

Starting with the left side:

\[ -(2x + 8) = -2x - 8 \]

Now, simplifying the right side:

\[ -3(-x + 1) = 3x - 3 \]

Now we can rewrite the equation as:

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

Next, we'll isolate the variable \( x \). Start by adding \( 2x \) to both sides:

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

This simplifies to:

\[ -8 = 5x - 3 \]

Next, add \( 3 \) to both sides:

\[ -8 + 3 = 5x - 3 + 3 \]

This simplifies to:

\[ -5 = 5x \]

Now, divide by \( 5 \):

\[ x = -1 \]

The solution in simplest form is:

\[ x = -1 \]

Since we found a specific value for \( x \), the answer is:

C: one solution.