Solve Addition Inequalities Quick Check
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3 of 5 Items
Question
Which of the following shows the graph of the solution to
x+3≤7
?(1 point)
Responses
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward negative 7 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward 13 with an arrow at the end.
The correct graph of the solution to x+3≤7 would be the image with alt text: A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward 13 with an arrow at the end.
The correct answer is: Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.
To solve the inequality x + 3 ≤ 7, we need to isolate the variable x.
First, we subtract 3 from both sides of the inequality:
x + 3 - 3 ≤ 7 - 3
This simplifies to:
x ≤ 4
Now, to represent this solution graphically, we can use a number line.
- Draw a number line with arrows at both ends.
- Mark a closed circle on the tick line above the number 4.
- Draw a line starting from 4 and going towards the left (in the negative direction) with an arrow at the end.
This graphically represents the solution to the inequality x + 3 ≤ 7.
Looking at the provided responses, the option that matches this graph description is the first one:
Image with alt text: A number line with arrows at both ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.