Question

What is the value of x in the equation ? 2.5(6x-4)=10+4(1.5+0.5x)

Answer 1

The value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x) is found by distributing the multipliers, combining like terms, and solving for x, which yields the solution x = 2.

Step-by-step explanation:

To determine the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x), the first step is to distribute the numbers inside each set of parentheses and then combine like terms.

Begin by expanding:

• 2.5 * 6x = 15x
• 2.5 * -4 = -10
• 4 * 1.5 = 6
• 4 * 0.5x = 2x

This leads to:

15x - 10 = 10 + 6 + 2x

Next, we combine like terms and isolate variables to one side:

15x - 2x = 10 + 6 + 10

13x = 26

Finally, we divide by 13 to find:

x = 2

The value of x is 2.

Answer 2

Step 1: Rewrite

2.5(6x-4)=10+4(1.5+0.5x)

Step 2: Distribute

Multiply 2.5 by 6 and then do the same to -4. MAKE SURE TO MULTIPLY 2.5 BY NEGATIVE 4 OR THE ANSWER WILL BE WRONG.

You should get:

15x-10=10+4(1.5+0.5x)

Step 3: Combine Like Terms

Look over the left side of the equation. If there are no numbers to combine, go to the right side. 10 and 4 are like terms. You may go ahead and combine them.

You should get:

15x-10=21+7x

Step 5: Combine Like Terms again

Now that you have no like terms on either side of the equation, you will combine them together. Confusing? Let me explain, you have a 15x and 7x on two sides of the equation and they are like terms. Since they are on different sides of the equation, you need to do the opposite of what you'd do if they were on the same side.

You should get:

8x=31

What I did was take the 7x (since its the lesser value) and subtract it by 15x and I got 8x. I then took the -10 and added it to 21.

Step 6: Divide

Now that you have 8x=31, you can simply divide and get your answer.

You should get:

x=3.875

Now, depending on what your problem is asking for, you would either round to the tenths or hundreths place.

There you go!