Solve: |2x + 3| -1 < 4

Mathematics

2 answers:

lara [203]3 years ago

8 0

Add 1
|2x +3| < 5
Unfold
-5 < 2x +3 < 5
Subtract 3
-8 < 2x < 2
Divide by 2
-4 < x < 1

The solution is
-4 < x < 1

_____
If you subtract 4 from both sides, you get an expression that compares to zero. Most graphing calculators will show you the zero-crossings, so you can easily find the values of x where this is true.

dybincka [34]3 years ago

7 0

|2x+3|-1<4
|2x+3|<5

1) when 2x +3 is positive
2x+3<5
2x<2
x<1 (-∞, 1)

2) when 2x+3 is negative
-(2x+3)<5
-2x-3<5
-2x<8
x>-4 (-4, ∞)

(-∞, 1)∩(-4, ∞)=(-4,1)

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The measures of 6 of the interior angles of a heptagon are: 120°, 150°, 135°, 170°, 90°, and 125°. What is the measure of the la

Lilit [14]

1. consider one angle of a (convex) heptagon. From that angle you can construct 7-3=4 diagonals. (-3 because we cannot create diagonals with the adjacent vertices and the angle itself )

2. 4 diagonals create 5 triangular regions. (check the picture)

3. So the sum of the measures of the interior angles of the heptagon is 180°*5=900°.

4. The measure of the remaining 7th interior angle is 900°-(120+150+135+170+90+125)°=110°.

5. The largest exterior angle is when the interior angle is the smallest.

6. The smallest interior angle is 90°, so the largest exterior angle is 180°-90°=90°

Answer: 90°