Determine the solution set of −3x+7=10 or 3x−9=0.(1 point)
A. The solution set is null.
B. {−1}
left brace negative 1 right brace
C. {3}
left brace 3 right brace
D. {−1,3}
To solve the equation −3x+7=10, we need to isolate x. Subtracting 7 from both sides, we get −3x = 3. Dividing by −3, we find x = -1.
To solve the equation 3x−9=0, we need to isolate x. Adding 9 to both sides, we get 3x = 9. Dividing by 3, we find x = 3.
Therefore, the solution set is {−1, 3}. Answer choice D.
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?
Based on the description of the number line graph, we can determine the solution set as follows:
- The open point at 3, with a solid line extending right beyond 5, indicates that the graph represents all the values greater than 3. However, it does not include 5 itself.
- The open point at -3, with a solid line extending left beyond -5, indicates that the graph represents all the values less than -3. However, it does not include -5 itself.
Combining these two ranges, we can determine that the solution set represented by the number line graph is {x | x < -3 or x > 3}. This means that the solution set includes all values to the left of -3 and all values to the right of 3. However, it does not include -3 or 3 themselves.
Therefore, the solution set represented by the number line graph is: {x | x < -3 or x > 3}.
To determine the solution set of the given equations, we will solve each equation separately and then combine their solution sets.
Equation 1: -3x + 7 = 10
Step 1: Subtract 7 from both sides:
-3x + 7 - 7 = 10 - 7
-3x = 3
Step 2: Divide both sides by -3 to solve for x:
-3x / -3 = 3 / -3
x = -1
Equation 2: 3x - 9 = 0
Step 1: Add 9 to both sides:
3x - 9 + 9 = 0 + 9
3x = 9
Step 2: Divide both sides by 3 to solve for x:
3x / 3 = 9 / 3
x = 3
Now, let's combine the solution sets of both equations: {-1, 3}
So, the answer is D. {−1,3}