All categories

2 years ago

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?

Mathematics

2 answers:

Romashka [77]2 years ago

7 0

Answer:

Step-by-step explanation:

Isolate x on one side of the equation.

1.5(x+4)-3=4.5(x-2)

1.5(x+4)*10-3*10=4.5(x-2)*10 (First, multiply 10 from both sides.)

15(x+4)-30=45(x-2) (Refine.)

15(x+4) (Expand by using distributive property.)

<u><em>DISTRIBUTIVE PROPERTY:</em></u>

A(B+C)=AB+AC

A(B-C)=AB-AC

15*x=15x

15*4=30

15x+30

45(x-2)

45*x=45

45*2=90

45x-90

15x+30=45x-90

15x+30-30=45x-90-30 (Subtract by 30 from both sides.)

90-30 (Solve.)

90+30=120

15x=45x-120

15x-45x=45x-120-45x (Subtract 45x from both sides.)

15x-45x (Solve.)

15x-45x=-30x

-30x=-120

-30x/-30=-120/-30 (Then, divide by -30 from both sides.)

-120/-30 (Solve.)

-120/-30=4

x=4

Therefore, the correct answer is x=4.

padilas [110]2 years ago

5 0

Answer:4

Step-by-step explanation:

First distributive 1.5 to x+4 and 4.5 to x-2. You get 1.5x+6-3 = 4.5x-9. Next you need to move all the variable terms to one side. You can do either, it doesn't matter, but I subtracted 1.5 x to each side of the equation. You get left with 6-3 = 3x-9. Solve 6-3 and you get 3=3x-9. You 9 to both sides of the equation. You get 12=3x. You divide by 3 on both sides and get 4=x/x=4.

You might be interested in

A 56-inch Woman cast a shadow that is 16 inches long. How tall is her child if his shadow is 14 inches long?

nikitadnepr [17]

Answer:49

Step by step is 56÷16=3.5

14x3.5=49

6 0

2 years ago

Which category do all of these shapes belong to

Nataly [62]

Answer:

squares

Step-by-step explanation:

4 0

3 years ago

Draw a picture of the standard normal curve and shade the area that corresponds to the requested probabilities. Then use the sta

elena-14-01-66 [18.8K]

Answer:

a)P [ z > 1,38 ] = 0,08379

b) P [ 1,233 < z < 2,43 ] = 0,1012

c) P [ z > -2,43 ] = 0,99245

Step-by-step explanation:

a) P [ z > 1,38 ] = 1 - P [ z < 1,38 ]

From z-table P [ z < 1,38 ] = 0,91621

P [ z > 1,38 ] = 1 - 0,91621

P [ z > 1,38 ] = 0,08379

b) P [ 1,233 - 2,43 ] must be P [ 1,233 < z < 2,43 ]

P [ 1,233 < z < 2,43 ] = P [ z < 2,43 ] - P [ z > 1,233 ]

P [ z < 2,43 ] = 0,99245

P [ z > 1,233 ] = 0,89125 ( approximated value without interpolation)

Then

P [ 1,233 < z < 2,43 ] = 0,99245 - 0,89125

P [ 1,233 < z < 2,43 ] = 0,1012

c) P [ z > -2,43 ]

Fom z-table

P [ z > -2,43 ] = 1 - P [ z < -2,43 ]

P [ z > -2,43 ] = 1 - 0,00755

P [ z > -2,43 ] = 0,99245

8 0

2 years ago

Please answer! I crossed out the ones you don’t have to complete.

Nina [5.8K]

Answer:

1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

5. $x^-6 = \frac{1}{x^6}$

6. $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7. $a^{-3}b^0c^4=\frac{c^4}{a^3}$

Step-by-step explanation:

Question 1:

We need to rewrite the expression using exponents

5.a.b.b.5.c.a.b.5.b

We will first combine the like terms

5.5.5.a.a.b.b.b.b.c

Now, if we have 5.5.5 we can write it in exponent as: $=5^{1+1+1}=5^3$

a.a as $a^{1+1}=a^2$

b.b.b.b as: $b^{1+1+1+1}=b^4$

So, our result will be:

$5^3a^2b^4c$

Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

Question:

Rewrite using positive exponent:

The rule used here will be: $a^{-1}=\frac{1}{a^1}$ which states that if we need to make exponent positive, we will take it to the denominator.

Applying thee above rule for getting the answers:

5) $x^{-6} = \frac{1}{x^6}$

6) $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7) $a^{-3}b^0c^4=\frac{b^0c^4}{a^3}$

We know that $b^0=1$ so, we get

$a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}$

4 0

3 years ago

Jada has read 3/5 of a book. She has read 75 pages so far. How many pages are in the whole book?

saveliy_v [14]

Answer:

125 pages

Step-by-step explanation:

we can use a proportion

3/5=75/x

multiply cross so 75×5 and 3×X

375=3x

÷3. ÷3

x=125

check

75/125=simplified is 3/5

7 0

3 years ago