2) If x + 6 < 32, subtract 6 from both sides, obtaining x < 26.
Draw a cirlce at x=26 and extend a ray from that x to the left.
graph c is 2x> 50 and graph b is x+6<32
For 2x>50 you first divide 50 by2 leaving you with x>25 therefore x is all numbers greater than 25.
For x+6<32 you first subtract 6 from 32 leaving you with x<26 therefore x is all numbers less than 26.
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2x > 50
Dividing both sides by 2:
x > 25 which is Graph C (because the red line is to the right of 25).
x + 6 < 32
x < 32 - 6
x < 26 which is Graph B .
Step-by-step explanation:Simplify the inequalities and match them with the graphs that represent them.
2x > 12
7x < 42
x + 1 < 8
3x > 15
the first one is graph c and the second, graph b.
They are both linear inequalities, so for both, you have to solve for x first. For the first one, since x is basically multiplied to 2 (2x), you have to divide both sides to get x by itself, and you get x>25. The graph has to have an opened circle, and the arrow should go to the right because all the numbers greater than 25 can be x. For the second one, you have to subtract 6 to both sides to get x by itself which then leaves you with ×<26. This one should also be an opened circle, and is going to the left, because all the numbers less than 26 can be x.
The first inequality is given by:
on dividing both side of the inequality by 2 we obtain:
i.e. the solution set is the set of all the real values which are strictly greater than 25.
i.e. the shaded region is to the tight of 25 and there will be a open circle at 25 (Since the inequality is strict inequality )
i.e. the solution set is: (25,∞)
Hence, the graph which represents the inequality 2x>50 is: Graph C.
The second inequality is given by:
on subtracting both side of the inequality by 6 we get:
This means that the solution set is the set of all the real values which are strictly less than 26.
i.e. the shaded region is to the left of 26 and there will be a open circle at 26 ( since the inequality is strict)
i.e. the solution set is: (-∞,26)
The graph which represents the inequality x+6<32 is: Graph B