Determine the solution set of −3x+7=10 or 3x−9=0.(1 point)

Question

Responses

{3}
left brace 3 right brace

The solution set is null.
The solution set is null.

{−1}
left brace negative 1 right brace

{−1,3}

Answer 1

To find the solution set for the equations \( -3x + 7 = 10 \) or \( 3x - 9 = 0 \), we will solve each equation separately.

1. Solving the first equation: \[ -3x + 7 = 10 \] Subtract 7 from both sides: \[ -3x = 3 \] Divide by -3: \[ x = -1 \]

2. Solving the second equation: \[ 3x - 9 = 0 \] Add 9 to both sides: \[ 3x = 9 \] Divide by 3: \[ x = 3 \]

Now, we have two solutions: \( x = -1 \) from the first equation and \( x = 3 \) from the second equation.

Thus, the solution set is: \[ { -1, 3 } \]

The correct response is: {−1,3}

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 3, with a solid line extending right, beyond 5. An open point is plotted at negative 3, with a solid line extending left, beyond negative 5.

What solution set does the number line graph?

(1 point)
Responses

x<−3 or x>3
x less than negative 3 or x greater than 3

x≤−3 and x≥−3
x less-than-or-equal-to negative 3 and x greater-than-or-equal-to negative 3

x<−3 and x>3
x less than negative 3 and x greater than 3

x≤−3 or x≥−3

Answer 3

Based on the description of the number line:

1. An open point at \(3\) indicates that \(x\) can be greater than \(3\) but not equal to \(3\). This means the inequality is \(x > 3\).
2. An open point at \(-3\) indicates that \(x\) can be less than \(-3\) but not equal to \(-3\). This means the inequality is \(x < -3\).

The solid lines extending from these points represent the range of values that satisfy the conditions specified.

Combining these two parts, the solution set represented on the number line is: \[ x < -3 \quad \text{or} \quad x > 3 \]

So the correct response is: x < −3 or x > 3

Answer 4

Use the image to answer the question.

A number line ranges from negative 10 to 2 in increments of 1. Two open points are plotted at negative 8 and negative 2, with a solid line extending between them.

Select the solution set represented on the graph.

(1 point)
Responses

x≥−8 or x≤−2
x greater-than-or-equal-to negative 8 or x less-than-or-equal-to negative 2

x>−8 and x<−2
x greater than negative 8 and x less than negative 2

x≥−8 and x≤−2
x greater-than-or-equal-to negative 8 and x less-than-or-equal-to negative 2

x>−8 or x<−2

Answer 5

Based on the description of the number line:

1. There are open points at \(-8\) and \(-2\), which indicates that these points are not included in the solution set.
2. A solid line extending between \(-8\) and \(-2\) indicates that the values between \(-8\) and \(-2\) are included in the solution set.

Thus, the inequalities represented are:

• For the value at \(-8\): \(x > -8\) (since it's an open point)
• For the value at \(-2\): \(x < -2\) (since it's also an open point)

Combining these conditions, we arrive at the solution set: \[ x > -8 \quad \text{and} \quad x < -2 \]

The correct response is: x > −8 and x < −2

Answer 6

Use the image to answer the question.

A number line ranges from 1 to 13 in increments of 1. A closed point is plotted at 10, with a solid line extending right, beyond 13. A closed point is plotted at 9, with a solid line extending left, beyond 1.

Select the solution set represented on the graph.

(1 point)
Responses

m≥10 and m≤9
m greater-than-or-equal-to 10 and m less-than-or-equal-to 9

m>10 or m<9
m greater than 10 or m less than 9

m>10 and m<9
m greater than 10 and m less than 9

m≥10 or m≤9

Answer 7

Based on the description of the number line:

1. A closed point at \(10\) means that \(m\) can be equal to \(10\) or greater than \(10\). This indicates the inequality \(m \geq 10\) with a solid line extending to the right, which shows that the values extend indefinitely beyond \(10\).

2. A closed point at \(9\) means that \(m\) can be equal to \(9\) or less than \(9\). This indicates the inequality \(m \leq 9\) with a solid line extending to the left, showing that the values go indefinitely below \(9\).

Considering these conditions together, the solution set represented on the graph is: \[ m \geq 10 \quad \text{or} \quad m \leq 9 \]

Since both inequalities are connected with "or", the correct response is: m ≥ 10 or m ≤ 9