Solve the inequality and graph the solution on the line provided.

Question

3, x, plus, 41, is greater than, 56
3x+41>
56
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 1

To solve the inequality \( 3x + 41 > 56 \), we'll follow these steps:

1. Subtract 41 from both sides: \[ 3x + 41 - 41 > 56 - 41 \] \[ 3x > 15 \]

2. Divide both sides by 3: \[ \frac{3x}{3} > \frac{15}{3} \] \[ x > 5 \]

So, the solution to the inequality is \( x > 5 \).

Inequality Notation:
\( x > 5 \)

Number Line:
To graph this solution on a number line:

• Draw a number line.
• Place an open circle on the number 5 to indicate that 5 is not included in the solution (since it's greater than, not greater than or equal to).
• Shade to the right of the open circle to indicate all numbers greater than 5.

This visually represents that the solution includes all values greater than 5.

Answer 2

Solve the inequality and graph the solution on the line provided.
8, x, minus, 2, is greater than or equal to, 14
8x−2≥
14
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 3

To solve the inequality \( 8x - 2 \geq 14 \), we will follow these steps:

1. Add 2 to both sides: \[ 8x - 2 + 2 \geq 14 + 2 \] \[ 8x \geq 16 \]

2. Divide both sides by 8: \[ \frac{8x}{8} \geq \frac{16}{8} \] \[ x \geq 2 \]

So, the solution to the inequality is \( x \geq 2 \).

Inequality Notation:
\( x \geq 2 \)

Number Line:
To graph this solution on a number line:

• Draw a number line.
• Place a closed circle on the number 2 to indicate that 2 is included in the solution (since it’s greater than or equal to).
• Shade to the right of the closed circle to indicate all numbers greater than or equal to 2.

This visually represents that the solution includes all values equal to or greater than 2.

Answer 4

Solve for xx:
minus, 2, x, plus, 6, equals, minus, x, plus, 3
−2x+6=
−x+3

Answer 5

To solve the equation \( -2x + 6 = -x + 3 \), we will isolate \( x \) by following these steps:

1. Add \( x \) to both sides to eliminate the \( -x \) on the right side: \[ -2x + x + 6 = 3 \] This simplifies to: \[ -x + 6 = 3 \]

2. Subtract 6 from both sides to isolate the term with \( x \): \[ -x + 6 - 6 = 3 - 6 \] This simplifies to: \[ -x = -3 \]

3. Multiply both sides by \( -1 \) to solve for \( x \): \[ x = 3 \]

So, the solution is: \[ \boxed{x = 3} \]

Answer 6

Question

Solve for xx:
3, x, plus, 1, equals, minus, 2, x, plus, 36
3x+1=
−2x+36

Answer 7

To solve the equation \( 3x + 1 = -2x + 36 \), follow these steps:

1. Add \( 2x \) to both sides to eliminate the \( -2x \) on the right side: \[ 3x + 2x + 1 = 36 \] This simplifies to: \[ 5x + 1 = 36 \]

2. Subtract 1 from both sides to isolate the term with \( x \): \[ 5x + 1 - 1 = 36 - 1 \] This simplifies to: \[ 5x = 35 \]

3. Divide both sides by 5 to solve for \( x \): \[ x = \frac{35}{5} \] This simplifies to: \[ x = 7 \]

So, the solution is: \[ \boxed{x = 7} \]

Answer 8

Solve.
2, left parenthesis, 7, z, minus, 6, right parenthesis, equals, 44
2(7z−6)=
44
find Z

Answer 9

To solve the equation \( 2(7z - 6) = 44 \), follow these steps:

1. Distribute the 2 on the left side: \[ 2 \cdot 7z - 2 \cdot 6 = 44 \] This simplifies to: \[ 14z - 12 = 44 \]

2. Add 12 to both sides to isolate the term with \( z \): \[ 14z - 12 + 12 = 44 + 12 \] This simplifies to: \[ 14z = 56 \]

3. Divide both sides by 14 to solve for \( z \): \[ z = \frac{56}{14} \] This simplifies to: \[ z = 4 \]

So, the solution is: \[ \boxed{z = 4} \]

Answer 10

Solve.
9, left parenthesis, y, minus, 8, right parenthesis, equals, 18
9(y−8)=
18
find y

Answer 11

To solve the equation \( 9(y - 8) = 18 \), follow these steps:

1. Divide both sides by 9 to simplify the equation: \[ y - 8 = \frac{18}{9} \] This simplifies to: \[ y - 8 = 2 \]

2. Add 8 to both sides to isolate \( y \): \[ y - 8 + 8 = 2 + 8 \] This simplifies to: \[ y = 10 \]

So, the solution is: \[ \boxed{y = 10} \]