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kherson [118]
3 years ago
8

would someone be able to explain to me how to solve these problems? I don't need the solutions, I just need an explanation. I ne

ed to solve the quadratic by factoring.

Mathematics
1 answer:
Leni [432]3 years ago
8 0
The first 3  are examples of the difference of 2 squares so you use the identity 
a^2 - b^2 = (a + b)(a - b)
x^2 - 49 = 0 
so (x + 7)(x - 7) = 0
so either x + 7 = 0 or x - 7 = 0
giving x = -7  and 7.
Number 7 reduces to 3x^2 =12, x^2  = 4 so x = +/- 2
Number 8  take out GCf (d) to give 
d(d - 2)  = 0   so d = 0 ,  2
9 and 10 are more difficult to factor
you use the 'ac' method  Google it to get more details
2x^2 - 5x + 2
multiply first coefficient by the constant at the end 
that is 2 * 2 =  4
Now we want  2 numbers  which when multiplied give + 4 and when added give - 5:-    -1 and -4  seem promising so we write the equation as:-

2x^2 - 4x - x + 2 = 0

now factor by grouping 
2x(x - 2) - 1(x - 2) = 0

(x - 2) is common so

(2x - 1)(x - 2) = 0
and 2x - 1 = 0 or x - 2 = 0  and now you can find x.

The last example is solved in the same way.


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Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.
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Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is  (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

  • if |a|> b then a>b or a<-b
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So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

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