Question

select all the equations that have no solution. 2 + 4(4x + 5) = 8x + 2x - 11; -x + 3x - 7 = 2(x - 7); 7 - 5x(-3) = 5(3x - 2); 6x + 3(2x - 1) = 5x - 4 + 7x + 1

Explanation:

To determine which equations have no solution, we solve each equation:

Equation 1: \( 2 + 4(4x + 5) = 8x + 2x - 11 \)

Step 1: Simplify both sides

Left side: \( 2 + 16x + 20 = 16x + 22 \)
Right side: \( 10x - 11 \)

Step 2: Solve for \( x \)

\( 16x + 22 = 10x - 11 \)
Subtract \( 10x \): \( 6x + 22 = -11 \)
Subtract \( 22 \): \( 6x = -33 \)
Divide by \( 6 \): \( x = -\frac{33}{6} = -\frac{11}{2} \)
This equation has a solution.

Equation 2: \( -x + 3x - 7 = 2(x - 7) \)

Step 1: Simplify both sides

Left side: \( 2x - 7 \)
Right side: \( 2x - 14 \)

Step 2: Solve for \( x \)

\( 2x - 7 = 2x - 14 \)
Subtract \( 2x \): \( -7 = -14 \)
This is a contradiction (false statement), so the equation has no solution.

Equation 3: \( 7 - 5x(-3) = 5(3x - 2) \)

Step 1: Simplify both sides

Left side: \( 7 + 15x \)
Right side: \( 15x - 10 \)

Step 2: Solve for \( x \)

\( 7 + 15x = 15x - 10 \)
Subtract \( 15x \): \( 7 = -10 \)
This is a contradiction (false statement), so the equation has no solution.

Equation 4: \( 6x + 3(2x - 1) = 5x - 4 + 7x + 1 \)

Step 1: Simplify both sides

Left side: \( 6x + 6x - 3 = 12x - 3 \)
Right side: \( 12x - 3 \)

Step 2: Solve for \( x \)

\( 12x - 3 = 12x - 3 \)
Subtract \( 12x \): \( -3 = -3 \)
This is an identity (true for all \( x \)), so the equation has infinitely many solutions.

Final Answer:

The equations with no solution are:

• \( -x + 3x - 7 = 2(x - 7) \)
• \( 7 - 5x(-3) = 5(3x - 2) \)

So the correct checkboxes are for these two equations.

Answer:

To determine which equations have no solution, we solve each equation:

Equation 1: \( 2 + 4(4x + 5) = 8x + 2x - 11 \)

Step 1: Simplify both sides

Left side: \( 2 + 16x + 20 = 16x + 22 \)
Right side: \( 10x - 11 \)

Step 2: Solve for \( x \)

\( 16x + 22 = 10x - 11 \)
Subtract \( 10x \): \( 6x + 22 = -11 \)
Subtract \( 22 \): \( 6x = -33 \)
Divide by \( 6 \): \( x = -\frac{33}{6} = -\frac{11}{2} \)
This equation has a solution.

Equation 2: \( -x + 3x - 7 = 2(x - 7) \)

Step 1: Simplify both sides

Left side: \( 2x - 7 \)
Right side: \( 2x - 14 \)

Step 2: Solve for \( x \)

\( 2x - 7 = 2x - 14 \)
Subtract \( 2x \): \( -7 = -14 \)
This is a contradiction (false statement), so the equation has no solution.

Equation 3: \( 7 - 5x(-3) = 5(3x - 2) \)

Step 1: Simplify both sides

Left side: \( 7 + 15x \)
Right side: \( 15x - 10 \)

Step 2: Solve for \( x \)

\( 7 + 15x = 15x - 10 \)
Subtract \( 15x \): \( 7 = -10 \)
This is a contradiction (false statement), so the equation has no solution.

Equation 4: \( 6x + 3(2x - 1) = 5x - 4 + 7x + 1 \)

Step 1: Simplify both sides

Left side: \( 6x + 6x - 3 = 12x - 3 \)
Right side: \( 12x - 3 \)

Step 2: Solve for \( x \)

\( 12x - 3 = 12x - 3 \)
Subtract \( 12x \): \( -3 = -3 \)
This is an identity (true for all \( x \)), so the equation has infinitely many solutions.

Final Answer:

The equations with no solution are:

• \( -x + 3x - 7 = 2(x - 7) \)
• \( 7 - 5x(-3) = 5(3x - 2) \)

So the correct checkboxes are for these two equations.