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3 years ago

What is the justification for the step taken from line 2 to line 3?

Mathematics

2 answers:

stiv31 [10]3 years ago

3 0

Step-by-step explanation:

$3x+9-7x=x+10+x\\-4x+9=2x+10\\-6x+9=10\\$

In the line 2, only variables were operated with a reduction of similar terms in each side of the equation, giving as result -4x at one side, and 2x at the other side.
In the line 3, terms with variables were joined together in one side of the equation, and then, they were operate it, given as result -6X.

brilliants [131]3 years ago

3 0

Answer:

the subtraction property of equality

Step-by-step explanation:

up up up uppity

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Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. Th

zvonat [6]

The labor fee is $13.55 and each quart of oil is $2.25

Step-by-step explanation:

Let,

x be the amount of each quart of oil

y be the amount of labor fee

According to given statement;

5x+y=24.80 Eqn 1

7x+y=29.30 Eqn 2

Subtracting Eqn 1 from Eqn 2

$(7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50$

Dividing both sides by 2

$\frac{2x}{2}=\frac{4.50}{2}\\x=2.25$

Putting x=2.25 in Eqn 1

$5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55$

The labor fee is $13.55 and each quart of oil is $2.25

Keywords: linear equation, subtraction

Learn more about subtraction at:

#LearnwithBrainly

6 0

3 years ago

Solve the following equation by completing the square. 3x^2-3x-5=13

mr Goodwill [35]

we'll start off by grouping some

$\bf 3x^2-3x-5=13\implies (3x^2-3x)-5=13\implies 3(x^2-x)-5=13 \\\\\\ 3(x^2-x)=18\implies (x^2-x)=\cfrac{18}{3}\implies (x^2-x)=6\implies (x^2-x+~?^2)=6$

so we have a missing guy at the end in order to get the a perfect square trinomial from that group, hmmm, what is it anyway?

well, let's recall that a perfect square trinomial is

$\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2$

so we know that the middle term in the trinomial, is really 2 times the other two without the exponent, well, in our case, the middle term is just "x", well is really -x, but we'll add the minus later, we only use the positive coefficient and variable, so we'll use "x" to find the last term.

$\bf \stackrel{\textit{middle term}}{2(x)(?)}=\stackrel{\textit{middle term}}{x}\implies ?=\cfrac{x}{2x}\implies ?=\cfrac{1}{2}$

so, there's our fellow, however, let's recall that all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add (1/2)², we also have to subtract (1/2)²

$\bf \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2-\left[ \cfrac{1}{2} \right]^2 \right)=6\implies \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2 \right)-\left[ \cfrac{1}{2} \right]^2=6 \\\\\\ \left(x-\cfrac{1}{2} \right)^2=6+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{25}{4}\implies x-\cfrac{1}{2}=\sqrt{\cfrac{25}{4}} \\\\\\ x-\cfrac{1}{2}=\cfrac{\sqrt{25}}{\sqrt{4}}\implies x-\cfrac{1}{2}=\cfrac{5}{2}\implies x=\cfrac{5}{2}+\cfrac{1}{2}\implies x=\cfrac{6}{2}\implies \boxed{x=3}$