Simplify x + 3x

5-4. Solve each of the following equations for the indicated variable. Use your Equation Mat if it is helpful. Write down each o

balu736 [363]

QUESTION 1

The given equation is :

$2(y - 3) = 4$
We want to solve for y. This means we have to isolate y on one side of the equation while all other constants are also on the other side of the equation,

We first divide both sides by 2 to obtain,

$\frac{2(y - 3)}{2} = \frac{4}{2}$

We cancel out the common factors to get,

$y - 3 = 2$

We now group like terms to get,

$y = 3 + 2$

We simplify to obtain,

$y = 5$

QUESTION 2

The given equation is

$2x + 5y = 10$
We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

This implies that,

$2x= 10 - 5y$

We now divide through by 2, to obtain,

$\frac{2x}{2} = \frac{10}{2} - \frac{5y}{2}$

This will now give us,

$x = 5 - \frac{5}{2} y$

QUESTION 3

The given equation is
$6x + 3y = 4y + 11$

We want to solve for y. This means that we need to isolate y on one side of the equation, while all other variables and constants are also on the other side of the equation.

We first of all group all the y terms on one side of the equation to obtain,

$6x - 11 = 4y - 3y$

We simplify to get,

$6x - 11 = y$

This implies that,

$y = 6x - 11$

QUESTION 4

The given equation is,

$3(2x + 4) = 2 + 6x + 10$

We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

Let us first expand the brackets to get,

$6x + 12 = 2 + 6x + 10$
This implies that

$6x + 12 = 6x + 12$

We group like terms to get,

$6x - 6x = 12 - 12$

We now simplify both sides to get,

$0x = 0$

We don't want x to vanish, so let us try to divide both sides by zero to get,

$x = \frac{0}{0}$

This is an indeterminate form, which implies that, x has infinitely many solutions. This means that all the real numbers are solution to the equation.

$\therefore \: x \in \: R$

QUESTION 5

The given equation is,

$y = - 3x + 6$

We want to solve for x, so we add the additive inverse of 6, which is -6 to both sides of the equation to get,

$y - 6 = - 3x$

We rewrite this to obtain,

$- 3x = y - 6$

We divide through by -3 to get,

$\frac{ - 3x}{ - 3} = \frac{y}{ - 3} - \frac{6}{ - 3}$

This will give us,

$x = - \frac{y}{3} + 2$

or

$x= 2 - \frac{1}{3} y$

5 0

3 years ago

A rectangular prism has a length of 4 in., a width of 2 in., and a height of 212 in.

snow_lady [41]

Answer:

V = 1696 in3

Step-by-step explanation:

your asking how many cubes are needed to fill the rectangle which just means your asking for the volume, if you multiply L*W*H you'll get the answer

hope that helps

8 0

3 years ago

How do I construct angle XYZ with a measure of 2 times the measure of angle ABC

Serjik [45]

I can’t understand why everyone complicates this question. It can be easily solved by similar triangles.

In this png, we have something to make sure.

∠B=∠DAB
∠
B
=
∠
D
A
B
(Yes, dab)

This also means AD=BD
A
D
=
B
D
.

This is our basic construction of D, which is going to help us.

∠ADC=∠DAB+∠B=2∠B=∠CAB
∠
A
D
C
=
∠
D
A
B
+
∠
B
=
2
∠
B
=
∠
C
A
B

∠CAD=∠CAB−∠DAB=∠B
∠
C
A
D
=
∠
C
A
B
−
∠
D
A
B
=
∠
B

These are based on the fact that ∠A=2×∠B
∠
A
=
2
×
∠
B

Actually these conditions suffice. Because I am just proving that △ACD∼△BCA
△
A
C
D
∼
△
B
C
A

Similarity makes us realize the following:

ACBC=ADAB
A
C
B
C
=
A
D
A
B

and

ACBC=CDAC
A
C
B
C
=
C
D
A
C

So

AC×AB=BC×AD
A
C
×
A
B
=
B
C
×
A
D

and

AC2=BC×CD
A
C
2
=
B
C
×
C
D

So

BC2=BC×(BD+CD)=BC×(AD+CD)
B
C
2
=
B
C
×
(
B
D
+
C
D
)
=
B
C
×
(
A
D
+
C
D
)

=AC×AB+AC2
=
A
C
×
A
B
+
A
C
2

Q.E.D.
2.4k Views ·

6 0

3 years ago

It is important to know the appropriate dose of ibuprofen for a child so that you are ready in the case of high fever. The dosin

Alexus [3.1K]

Answer:

102 mg

Step-by-step explanation:

Let's convert 28 pounds to kgs.

Since 1 kg = 2.2 pounds, we can find:

$\frac{1Kg}{2.2Pounds}=\frac{xKg}{28Pounds}\\1*28=2.2x\\28=2.2x\\x=\frac{28}{2.2}\\x=12.73$

So 28 pounds is 12.73 Kg

Since 8mg is given per kg, for 12.73 kg, the amount given should be:

12.73 * 8 = 101.84

Rounded to nearest whole number, that is, 102 mg

8 0

4 years ago

Read 2 more answers

I need help with this

djyliett [7]

Answer:I don't know this one.

Step-by-step explanation:

7 0

3 years ago

Simplify x + 3x - 36