Determine the solution set of 2x>−8 and −5x+7=12 .(1 point) Responses {−1} left brace negative 1 right brace {x|x>−4} left brace x vertical bar x greater than negative 4 right brace {x|x>−1} left brace x vertical bar x greater than negative 1 right brace {−4}
To determine the solution set, we need to solve each equation individually and then find the intersection of the solution sets.
For the first equation, 2x > -8, we can divide both sides by 2 to get x > -4.
For the second equation, -5x + 7 = 12, we subtract 7 from both sides and then divide by -5 to get x = -1.
The solution set of the first equation is {x | x > -4}, which represents all numbers greater than -4.
The solution set of the second equation is {x | x = -1}, which represents only the number -1.
To find the intersection of these two solution sets, we can see that the only number that satisfies both x > -4 and x = -1 is -1.
Therefore, the solution set to the system of equations is {x | x = -1}.
Determine the solution set of −3x+7=10 or 3x−9=0 .(1 point) Responses {−1,3} left brace negative 1 comma 3 right brace {−1} left brace negative 1 right brace The solution set is null. The solution set is null. {3}
To determine the solution set of the system of equations −3x + 7 = 10 or 3x − 9 = 0, we need to solve each equation separately and then find the union of the solution sets.
Solving the first equation, we can subtract 7 from both sides, resulting in -3x = 3, and then divide by -3 to get x = -1.
Solving the second equation, we can solve for x by adding 9 to both sides, resulting in 3x = 9, and then dividing by 3 to get x = 3.
The solution set for the first equation is {x | x = -1}, which represents only the number -1.
The solution set for the second equation is {x | x = 3}, which represents only the number 3.
To find the union of these solution sets, we can combine the numbers -1 and 3.
Therefore, the solution set to the system of equations is {x | x = -1, 3}.
Use the image to answer the question. What solution set does the number line graph? (1 point) Responses x≤−3 or x≥−3 x less-than-or-equal-to negative 3 or 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 x less than negative 3 or x greater than 3 x≤−3 and x≥−3
The image is not provided, so I cannot answer the question based on the given information. Please provide the image or describe the graph shown on the number line.
To find the solution set for the given system of inequalities and equations:
1. Solve the inequality 2x > -8:
Divide both sides by 2 to isolate x:
x > -8/2
x > -4
So the solution to the first inequality is {x|x > -4}.
2. Solve the equation -5x + 7 = 12:
Subtract 7 from both sides to isolate the variable:
-5x = 12 - 7
-5x = 5
Divide both sides by -5:
x = 5/-5
x = -1
So the solution to the equation is {x|x = -1}.
Now, let's find the common solution from the solutions of both the inequality and the equation:
The common solution is the intersection of both sets of solutions.
By comparing the two solution sets, we find that the common solution is {x|x > -1}.
Therefore, the solution set for the given system of inequalities and equations is {x|x > -1}.
To determine the solution set of the given equations, let's solve them step by step:
1. Solve the inequality 2x > -8:
- Divide both sides of the inequality by 2 to isolate x: x > -4.
2. Solve the equation -5x + 7 = 12:
- Subtract 7 from both sides to isolate the variable term: -5x = 5.
- Divide both sides of the equation by -5: x = -1.
So, we have two separate solutions for x: x > -4 and x = -1.
The solution set is the combination of these two solutions, represented using set notation {} or interval notation []:
{x | x > -4} or (-∞, -4) (open interval) denotes all the values of x that are greater than -4.
{x | x = -1} or [-1, -1] (closed interval) represents the single value x = -1.
Therefore, the solution set for the given equations is: {-1, x | x > -4} or {-1} ∪ (-∞, -4) or [-1] ∪ (-∞, -4).