What is the solution to the equation 0.24(x−10.2)=6 when solving for x ?(1 point)

Question

Responses

11.64
11.64

35.2
35.2

16.44
16.44

14.8

Answer 1

To solve the equation \( 0.24(x - 10.2) = 6 \) for \( x \), follow these steps:

1. Start by isolating the term with \( x \). Divide both sides of the equation by \( 0.24 \):

\[ x - 10.2 = \frac{6}{0.24} \]

2. Calculate \( \frac{6}{0.24} \):

\[ \frac{6}{0.24} = 25 \]

So now we have:

\[ x - 10.2 = 25 \]

3. Now, add \( 10.2 \) to both sides to find \( x \):

\[ x = 25 + 10.2 \]

4. Calculate \( 25 + 10.2 \):

\[ x = 35.2 \]

Thus, the solution to the equation is:

\[ \boxed{35.2} \]

Answer 2

Solve for x in the equation 811(x+45)=2455 .

Answer 3

To solve the equation \( 811(x + 45) = 2455 \) for \( x \), follow these steps:

1. Start by isolating the term that contains \( x \). Divide both sides of the equation by \( 811 \):

\[ x + 45 = \frac{2455}{811} \]

2. Calculate \( \frac{2455}{811} \):

\[ \frac{2455}{811} = 3.024 \quad \text{(approximately)} \]

This gives us:

\[ x + 45 \approx 3.024 \]

3. Next, subtract \( 45 \) from both sides to solve for \( x \):

\[ x \approx 3.024 - 45 \]

4. Calculate \( 3.024 - 45 \):

\[ x \approx -41.976 \]

So, the solution to the equation is approximately:

\[ x \approx -41.976 \]

If you need an exact answer instead, here it is in fractional form:

\[ x = \frac{2455}{811} - 45 \]

Now, converting \( 45 \) to a fraction with a denominator of \( 811 \):

\[ 45 = \frac{36495}{811} \]

Now substitute:

\[ x = \frac{2455 - 36495}{811} = \frac{-34040}{811} \]

So, the exact solution is:

\[ x = \frac{-34040}{811} \]

And the approximate solution is:

\[ \boxed{-41.976} \]

Answer 4

Solve for x in the equation 8/11(x+4/5)=24/55 .

Answer 5

To solve the equation \( \frac{8}{11}(x + \frac{4}{5}) = \frac{24}{55} \) for \( x \), follow these steps:

1. First, eliminate the fraction on the left side by multiplying both sides by the reciprocal of \(\frac{8}{11}\), which is \(\frac{11}{8}\):

\[ x + \frac{4}{5} = \frac{11}{8} \cdot \frac{24}{55} \]

2. Calculate the right side:

\[ \frac{11 \cdot 24}{8 \cdot 55} = \frac{264}{440} \]

3. Simplify the fraction \(\frac{264}{440}\) by finding the greatest common divisor (GCD) of \(264\) and \(440\), which is \(88\):

\[ \frac{264 \div 88}{440 \div 88} = \frac{3}{5} \]

So we have:

\[ x + \frac{4}{5} = \frac{3}{5} \]

4. Now, isolate \( x \) by subtracting \( \frac{4}{5} \) from both sides:

\[ x = \frac{3}{5} - \frac{4}{5} \]

5. Perform the subtraction:

\[ x = \frac{3 - 4}{5} = \frac{-1}{5} \]

Thus, the solution to the equation is:

\[ \boxed{-\frac{1}{5}} \]

Answer 6

What is the solution to the equation 1.26(x−7.352)=6.426 when solving for x?(1 point)
Responses

−2.252
negative 2.252

12.452
12.452

15.44876
15.44876

15.038

Answer 7

To solve the equation \( 1.26(x - 7.352) = 6.426 \) for \( x \), follow these steps:

1. First, divide both sides of the equation by \( 1.26 \) to isolate \( (x - 7.352) \):

\[ x - 7.352 = \frac{6.426}{1.26} \]

2. Calculate \( \frac{6.426}{1.26} \):

\[ \frac{6.426}{1.26} = 5.1 \]

So we now have:

\[ x - 7.352 = 5.1 \]

3. Next, add \( 7.352 \) to both sides to solve for \( x \):

\[ x = 5.1 + 7.352 \]

4. Perform the addition:

\[ x = 12.452 \]

Thus, the solution to the equation is:

\[ \boxed{12.452} \]

Answer 8

Solve for x in the equation  −6.29(x+7.85)=−19.499 .

Answer 9

To solve the equation \( -6.29(x + 7.85) = -19.499 \) for \( x \), follow these steps:

1. Start by dividing both sides by \( -6.29 \) to isolate \( (x + 7.85) \):

\[ x + 7.85 = \frac{-19.499}{-6.29} \]

Since both sides are negative, dividing gives us a positive result:

\[ x + 7.85 = \frac{19.499}{6.29} \]

2. Calculate \( \frac{19.499}{6.29} \):

\[ \frac{19.499}{6.29} \approx 3.096 \]

So now we have:

\[ x + 7.85 \approx 3.096 \]

3. Now subtract \( 7.85 \) from both sides to solve for \( x \):

\[ x \approx 3.096 - 7.85 \]

4. Perform the subtraction:

\[ x \approx -4.754 \]

Thus, the solution to the equation is:

\[ \boxed{-4.754} \]

Answer 10

Bags of clementines have 12 each. For a party, Sal, Trisha, and Joe each brought bags of clementines. Altogether, there were 180 clementines. Sal brought 4 bags and Joe brought 6. Write the equation to determine how many bags Trisha brought, t .(2 points)
___(t+____) =____ 

Answer 11

To find out how many bags of clementines Trisha brought, we can set up an equation based on the information given.

1. Each bag of clementines contains 12 clementines.
2. Sal brought 4 bags, Joe brought 6 bags, and we are trying to determine how many bags Trisha brought, represented by \( t \).
3. The total number of clementines is 180.

Now, we can express the total number of clementines brought by Sal, Joe, and Trisha in terms of \( t \):

• Sal brought \( 4 \) bags, so the number of clementines he brought is \( 4 \times 12 = 48 \).
• Joe brought \( 6 \) bags, so the number of clementines he brought is \( 6 \times 12 = 72 \).
• Trisha brought \( t \) bags, so the number of clementines she brought is \( t \times 12 \).

Now, we can write the equation for the total number of clementines:

\[ (48 + 72 + 12t) = 180 \]

Combining \( 48 \) and \( 72 \) gives us \( 120 \), so we can simplify the equation to:

\[ (120 + 12t) = 180 \]

Now, if we format this according to the specified structure \( (t + ___) = ___ \), we can rewrite it as:

\[ (t + 10) \times 12 = 180 \]

Thus, filling in the blanks, the equation we can use to determine how many bags Trisha brought is:

\[ (t + 10) = 15 \]

So the answer in the requested format is:

\[ (t + 10) = 180 \]

Where \( 10 \) represents the total clementines from Sal and Joe divided by \( 12 \): \( 120 \div 12 \).

So you can summarize: \[ __ (t + 10) = 180 \]

Here, \( 10 \) is the total bags brought by Sal and Joe divided by \( 12 \).