Justify each step of this inequality by stating the property that was used to get to each step.
2 answers:
Answer:
See below.
Step-by-step explanation:
We have the inequality:
Step 1: Combining Like Terms:
Step 2: Distribute Property (on the left):
Step 3: Addition Property of Equality (Add 7r to both sides):
Step 4: Addition Property of Equality (Add 15 to both sides):
Step 5: Division Property of Equality (Divide both sides by 2):
And we're done!
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Answer:
Solution Set: (-2,5)
Step-by-step explanation:
The solution is x ≤ 8.
Solution:
Given expression:
x + 9 – 3 ≤ 14
To solve this inequality.
x + 9 – 3 ≤ 14
Subtract the numbers 9 – 3.
x + 6 ≤ 14
Subtract 6 on both sides of the inequality.
x + 6 – 6 ≤ 14 – 6
x ≤ 8
The solution is x ≤ 8.
Now, graph the solution.
The solution of the graph is attached below.
Answer:
We conclude that the equation of the line in the form will be:
Step-by-step explanation:
From the given graph, taking two points
- (0, 0)
- (10, 5)
Important Tip:
The slope-intercept form of the line equation
where
represents the slope
represents the y-intercept
1 of 3 steps:
Determine the slope
We need to find the slope of the line containing the points (0, 0) and (10, 5)
where is the slope between (x₁, y₁) and (x₂, y₂)
In our case,
- (x₁, y₁) = (0, 0)
- (x₂, y₂) = (10, 5)
substituting (x₁, y₁) = (0, 0) and (x₂, y₂) = (10, 5) in the slope formula
Refine
Thus, the slope of the line containing the points (0, 0) and (10, 5) is:
2 of 3 steps:
Determine the y-intercept
We can determine the y-intercept by determining the value of y at x = 0.
From the graph, it is clear that at x = 0 the value of y = 0.
Thus, the y-intercept of the line is:
3 of 3 steps:
Substitute the values in the slope-intercept form
Substitute the values and
in the slope-intercept form
Conclusion:
Therefore, we conclude that the equation of the line in the form will be: