What is the solution set of 2x−3=5

Question

and 5x+3>−12
?(1 point)
{
}

Answer 1

To find the solution set of the equations \(2x - 3 = 5\) and the inequality \(5x + 3 > -12\), we need to solve each equation independently and then find the intersection of the solution sets.

1. Solving the equation \(2x - 3 = 5\):

   \[ 2x - 3 = 5 \] Add 3 to both sides: \[ 2x = 8 \] Divide by 2: \[ x = 4 \]

2. Solving the inequality \(5x + 3 > -12\):

   \[ 5x + 3 > -12 \] Subtract 3 from both sides: \[ 5x > -15 \] Divide by 5: \[ x > -3 \]

3. Finding the solution set:

   The solution to the equation is \(x = 4\). The solution to the inequality is \(x > -3\).

   The value \(x = 4\) is greater than \(-3\), so it satisfies the inequality.

Thus, the solution set that satisfies both the equation and the inequality is:

\[ {4} \]

So the final answer is \({4}\).

Answer 2

Use the image to answer the question.

A number line ranges from negative 5 to 5 in increments of 1. An open point is plotted at 2, with a solid line extending right, beyond 5. An open point is plotted at 0, with a dotted line extending left, beyond negative 5.

What is the solution set to the inequalities on the graph?

(1 point)
x<
or x>

Answer 3

From the description of the number line:

1. There is an open point at 2 with a solid line extending right, which indicates that \( x \) is greater than 2. Thus, we can write this part as: \[ x > 2 \]

2. There is also an open point at 0 with a dotted line extending left, which indicates that \( x \) is less than 0. So, we can write this part as: \[ x < 0 \]

Putting this information together, the solution set for the inequalities on the graph is: \[ x < 0 \quad \text{or} \quad x > 2 \]

This means the solution set can be expressed as: \[ { x | x < 0 \text{ or } x > 2 } \]

Answer 4

Use the image to answer the question.

A number line extends from negative 5 to 5 in increments of 1.

To indicate the solution for x≥−1
and x<4
, where would you place circles on the graph? Enter the lesser value first.

(1 point)

Answer 5

To represent the inequalities \( x \geq -1 \) and \( x < 4 \) on a number line:

1. For \( x \geq -1 \):

   • Since this is a "greater than or equal to" condition, we would use a solid circle at \(-1\) to indicate that \(-1\) is included in the solution set. The line would extend to the right of \(-1\).

2. For \( x < 4 \):

   • Since this is a "less than" condition, we would use an open circle at \(4\) to indicate that \(4\) is not included in the solution set. The line would extend to the left of \(4\).

Therefore, the placement of the circles on the graph would be:

• A solid circle at \(-1\)
• An open circle at \(4\)

To answer your question about the notation, you would place the circles as follows:

• \(-1\) (solid circle)
• \(4\) (open circle)

In your specified format: \[ -1, 4 \]

Answer 6

Use the image to answer the question.

A number line ranges from negative 3 to 8 in increments of 1. Two closed points are plotted at negative 2 and 7, with a solid line extending between them.

What solution set does the graph represent?

(1 point)
x≤
and x≥

Answer 7

Based on your description of the number line:

1. Closed points at \(-2\) and \(7\) indicate that both endpoints are included in the solution set.
2. Since there is a solid line extending between \(-2\) and \(7\), it means that all values between these two points, as well as the endpoints, are part of the solution set.

Given this information, the solution set can be represented with the following inequalities:

• The left endpoint (-2) indicates \( x \geq -2 \).
• The right endpoint (7) indicates \( x \leq 7 \).

Thus, the solution set represented by this graph is:

\[ -2 \leq x \leq 7 \]

or written in the format you requested:

\[ x \geq -2 \quad \text{and} \quad x \leq 7 \]

So you would write:

\[ x \geq -2 \quad \text{and} \quad x \leq 7 \]