Graph the solution of the equation
b-11=-8
a.-4
b.-3
c.3
d.4
2z > -28
a.z > -56
b.z > -14
c.z < -14
d.z < 14
solve the equation or inequality
use the number line
> means you use an open circle at that point and shade to the right
they are all closed circles though
To graph the solution of the equation b - 11 = -8, we need to solve for b first.
Given: b - 11 = -8
Adding 11 to both sides of the equation, we get:
b - 11 + 11 = -8 + 11
This simplifies to:
b = 3
Therefore, the solution to the equation is b = 3.
To graph the solution, we plot the point (3, 0) on a number line:
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-4 -3 -2 -1 0 1 2 3 4
The point (3, 0) would be represented as a dot on the number line above the number 3.
Therefore, the correct option is c. 3.
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To graph the solution of the inequality 2z > -28, we need to solve for z first.
Given: 2z > -28
Dividing both sides of the inequality by 2, we get:
z > -28 / 2
Simplifying, we have:
z > -14
This tells us that z is greater than -14. To represent this on a number line, we plot an open circle at -14 and draw an arrow to the right, indicating that z can take any value greater than -14.
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-28 -14 0 14 28
The open circle at -14 indicates that z is not equal to -14, it is only greater than -14.
Therefore, the correct option is d. z < 14.
To graph the solution of the equation b - 11 = -8, we need to isolate the variable b. Here's how you can do it:
b - 11 = -8
First, add 11 to both sides of the equation to isolate the b-term.
b - 11 + 11 = -8 + 11
This simplifies to:
b = 3
So, the solution to the equation is b = 3.
To graph this, we can represent the solution on a number line. Mark the point 3 on the number line, and that will be the graph of the solution.
Now, let's move on to the second equation:
2z > -28
To find the solution to this inequality, we need to isolate the variable z. Follow the steps below:
2z > -28
Divide both sides of the inequality by 2 to isolate the z-term.
(2z)/2 > (-28)/2
This simplifies to:
z > -14
So, the solution to the inequality is z > -14.
To graph this, we represent all values of z that are greater than -14 on a number line with an open circle at -14. The open circle indicates that -14 is not included in the solution.
Then, we draw an arrow towards the right to show that any value greater than -14 is included in the solution.
Therefore, the graph of the solution to the inequality 2z > -28 is z > -14, which means option c.z < -14 is incorrect. The correct option is b.z > -14.