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3 years ago

Solve and check the linear equation. 3(x-2) + 8 = 2(x + 5)

Mathematics

1 answer:

ANEK [815]3 years ago

3 0

Answer:

x = 8

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

<u>Algebra I</u>

Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

3(x - 2) + 8 = 2(x + 5)

<u>Step 2: Solve for </u><em><u>x</u></em>

(Parenthesis) Distribute: 3x - 6 + 8 = 2x + 10
Combine like terms: 3x + 2 = 2x + 10
{Subtraction Property of Equality] Subtract 2x on both sides: x + 2 = 10
[Subtraction Property of Equality] Subtract 2 on both sides: x = 8

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

Substitute in <em>x</em>: 3(8 - 2) + 8 = 2(8 + 5)
(Parenthesis) Subtract/Add: 3(6) + 8 = 2(13)
Multiply: 18 + 8 = 26
Add: 26 = 26

Here we see that 26 does indeed equal 26.

∴ x = 8 is the solution to the equation.

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Answer:

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Step-by-step explanation:

For a couple of these, it is helpful to remember that (a-b) = -(b-a).

$\dfrac{5}{x+2}+\dfrac{25-x}{x^2-3x-10}=\dfrac{5(x-5)}{(x+2)(x-5)}+\dfrac{25-x}{(x+2)(x-5)}\\\\=\dfrac{5x-25+25-x}{(x+2)(x-5)}=\dfrac{4x}{x^2-3x-10}$

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$\displaystyle\frac{\left(\frac{x}{x-2}\right)}{\left(\frac{2x}{2-x}\right)}=\frac{x}{x-2}\cdot\frac{-(x-2)}{2x}=\frac{-x(x-2)}{2x(x-2)}=-\frac{1}{2}$

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2 years ago

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HELPP PLEASE FAST!! a store has televisions on sale for 20% off the original price. The original price of a television is 150 be

Margarita [4]

Method 1: A pure algebraic approach

The unknown in this problem is the percent of decrease. A percent of decrease is the percentage of the original price that was deducted from the original price to obtain the sale price. We could write a "word equation" for this process like this:

original price - (percent of decrease)(original price) = sale price

Since the percent of decrease is the unknown in this problem, we'll call the percent of decrease x%.

Here's what we know so far:

The original price was $200

The sale price was $170

The percent of increase was x%

Putting this information in our word equation gives us an algebraic equation:

200 - (x%)(200) = 170

What do we do with the percent sign in this equation? "Percent" means "out of 100", so x% means x out of 100, or . Now we have this:

200 - (200) = 170

Now we'll solve our equation:

200 - (200) = 170

200 - 2x = 170

-2x = -30

x = 15

So the percent of decrease is 15%

Method 2: A method involving pure arithmetic.

If we know the original price and the sale price, we can find the percent of decrease in two steps:

Find the amount of decrease

Divide the amount of decrease by the original amount

This will give us the percent of decrease (written as a decimal number). We can then write the decimal as an equivalent percent to find our final answer.

Let's use method 2 on the same problem:

Frank bought a new television set on sale. If the TV's original price was $200 and Frank paid $170 for the TV, what was the percent of decrease?

First, let's find the amount of decrease:

Amount of decrease = 200 - 170 = 30

So the price decreased by $30.

Next, we'll find the percent of decrease, and rewrite the decimal answer as a percent:

Percent of decrease = = = .15 = 15%

So the percent of decrease is 15%

Before we leave the problem, let's check our answer:

Original price = $200

Price reduced by 15% of original price = 200(.15) = $30

Sale price would then be = $200 - $30 = $170

Our answer checks. We're done! Me not know if correct.

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