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NikAS [45]
2 years ago
14

1.3x - 10= 0.8x - 8 solve for x

Mathematics
2 answers:
Neporo4naja [7]2 years ago
5 0

Answer:

x = 4

Step-by-step explanation:

1.3x - 10 = 0.8x - 8

start by getting all like terms to the same side

subtract 0.8 x from both sides, add 10 to both sides

0.5x = 2

divide both sides by 0.5

x = 4

OverLord2011 [107]2 years ago
3 0

Answer:

x = 4

Step-by-step explanation:

1.3x - 10 = 0.8x - 8

Add 10 to both sides.

1.3x = 0.8x + 2

Subtract 0.8x from both sides.

0.5x = 2

Divide by 0.5.

x = 4.

Proof:

1.3x - 10 = 0.8x - 8

1.3(4) - 10 = 0.8(4) - 8

5.2 - 10 = 3.2 - 8

-4.8 = -4.8

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Step-by-step explanation:

These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.

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<h3>Squaring</h3>

The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.

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The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.

  x = -1: √(-1+2) +1 = √(3(-1)+3)   ⇒   1+1 = 0 . . . . not true

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<h3>Substitution</h3>

Another way to solve this is using substitution for one of the radicals. We choose ...

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  x = u² -2 = 2² -2

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_____

<em>Additional comment</em>

Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.

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150*(0.46) = 69 blueberry muffins

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