Solve for x: |2x + 12| = 18

Solve the equation 3x-2 4 - 2x - 5- 1 + x 3 6

Nataly_w [17]

Answer:

$\boxed{\sf x=12}$

Step-by-step explanation:

$\sf \cfrac{3x-2}{4}-\cfrac{2x-5}{3}=\cfrac{1+x}{6}$

First, let's find the LCM of 4, 3, and 6.

How to find the LCM:

→ List multiples of each number.

→ Find the smallest number on each list.

4: 4, 8, 12, 16, 20, 24..

3: 3, 6, 9, 12, 15, 18, 21, 24, 27....

6: 6, 12, 18, 24, 30, 36, 42...

LCM: 12

_________

Now, we'll Multiply by LCM:

$\sf \cfrac{3x-2}{4}\times \:12-\cfrac{2x-5}{3}\times \:12=\cfrac{1+x}{6}\times \:12$

Simplify:

$\sf 3\left(3x-2\right)-4\left(2x-5\right)=2\left(x+1\right)$

Now, expand, Apply the Distributive property:

$\bold{ 3\left(3x-2\right)-4\left(2x-5\right)}$

$\sf 9x-6-8x+20$

Combine like terms:

$\sf x+14$

________

$\bold{ 2\left(x+1\right)}$

$\sf 2x+2$

$\sf x+14=2x+2$

Subtract 14 from both sides:

$\sf x+14-14=2x+2-14$

Simplify:

$\sf x=2x-12$

Subtract 2x from both sides:

$\sf x-2x=2x-12-2x$

Simplify:

$\sf -x=-12$

Divide both sides by -1:

$\sf \cfrac{-x}{-1}=\cfrac{-12}{-1}$

$\sf x=12$

7 0

2 years ago

Rename 5/6 and 14/15 using the least common denominator.

Vedmedyk [2.9K]

Answer:

25/30 and 28/30

Step-by-step explanation:

1. To find the least common denominator, you need to find the least common multiple of the two denominators which are 6 and 15. Prime factorization of these numbers gives:

6 = 2 x 3

15 = 5 x 3

A number that would evenly divide both 6 and 15 must contain 2 x 3 x 5 which is 30.

Thus 30 is the least common denominator.

2. Now we need to somehow change both fractions to make them have a denominator of 30. To do this we can multiply by fractions with same numerator and denominator since that would be like multiplying by 1.

So, 5/6 x 5/5 = 25/30

And 14/15 x 2/2 = 28/30

8 0

3 years ago

Y=1/2x + 3/4

Usimov [2.4K]

0,3/4

1/2,1

X being the first, y second term verify the equation

4 0

3 years ago

Add or subtract them in simplest form please help me as fast as possible

NARA [144]

Answer:

Okay so im seeing you need help okay I will tell you how to do number 21 as an example

Step-by-step explanation:

Look for a commen donominater of the 3/8 and 1/3 the denominater would be 24 so 8 times 3 and 3 times 3 so those would be 9/24 and 3/24 , do the 8 plus the ten and you get 18 so 18+ 9/24+3/24= 18 12/24, or 18 1/2

8 0

3 years ago

(Inequalities) what do you have to do when multiplying or dividing by a negative number?

Rashid [163]

Answer:

When we multiply or divide by a negative to solve an inequality, it's the same as multiplying or dividing by a negative to solve a regular equation! Just remember to multiply or divide both sides by the same quantity, then simplify! Remember, when multiplying or dividing by a negative YOU MUST FLIP THE INEQUALITY SIGN.

Step-by-step explanation:

You are welcome.

And I hope this helps. :)

4 0

3 years ago

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