Ask a New Question
Menu

Solve for x to determine if the equation has one, none, or infinite solutions. 11x=3(7x−1)−10x (1 point) Responses The equation has one solution: x=−1. The equation has one solution: x equals negative 1 . The equation has no solution. The equation has no solution. The equation has infinite solutions. The equation has infinite solutions. The equation has one solution: x=−3. HELP!

11 answers

Let's solve the equation step by step to find the value of \(x\):

The equation given is:

\[ 11x = 3(7x - 1) - 10x \]

First, distribute the \(3\) on the right side:

\[ 11x = 21x - 3 - 10x \]

Combine like terms on the right side:

\[ 11x = 21x - 10x - 3 \]

This simplifies to:

\[ 11x = 11x - 3 \]

Next, subtract \(11x\) from both sides:

\[ 11x - 11x = 11x - 11x - 3 \]

This simplifies to:

\[ 0 = -3 \]

Since this is a false statement (0 does not equal -3), it indicates that there is no value of \(x\) that satisfies the equation. Therefore, the equation has no solutions.

The correct response is: The equation has no solution.

Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−4=2x+6 (1 point) Responses The equation has one solution: x=0. The equation has one solution: x equals 0 . The equation has infinite solutions. The equation has infinite solutions. The equation has one solution: x=1. The equation has one solution: x equals 1 . The equation has no solution. The equation has no solution.

Let's solve the given equation step by step to find the value of \(x\):

The equation is:

\[ 5(2x + 2) - 4 = 2x + 6 \]

First, distribute the \(5\) on the left side:

\[ 10x + 10 - 4 = 2x + 6 \]

This simplifies to:

\[ 10x + 6 = 2x + 6 \]

Next, subtract \(2x\) from both sides:

\[ 10x - 2x + 6 = 6 \]

Which simplifies to:

\[ 8x + 6 = 6 \]

Next, subtract \(6\) from both sides:

\[ 8x = 0 \]

Now, divide both sides by \(8\):

\[ x = 0 \]

Since we found a specific solution for \(x\), the equation has one solution: \(x = 0\).

Thus, the correct response is: The equation has one solution: x=0.

Solve the following linear equation for x . Then check your answer. Show all your steps for solving and checking. 5x+8+x=32 (4 points) Do not give me long answer please. Make it very short and easy.

Sure! Here are the steps to solve the equation \(5x + 8 + x = 32\):

Step 1: Combine like terms

\[ 5x + x + 8 = 32 \implies 6x + 8 = 32 \]

Step 2: Subtract 8 from both sides

\[ 6x = 32 - 8 \implies 6x = 24 \]

Step 3: Divide by 6

\[ x = \frac{24}{6} \implies x = 4 \]

Step 4: Check the solution

Substitute \(x = 4\) back into the original equation: \[ 5(4) + 8 + 4 = 32 \implies 20 + 8 + 4 = 32 \implies 32 = 32 \]

The solution is correct.

Final Answer: \(x = 4\).

Describe three ways to write the ratio that compares 4 electronic devices for every 3 people.(1 point) Responses 4 to 3, 4:3, 43 4 to 3, ratio of 4 to 3 , Start fraction 4 over 3 end fraction 4 to 3, 4:3, 34 4 to 3, ratio of 4 to 3 , Start fraction 3 over 4 end fraction 3 to 4, 3:4, 34 3 to 4, ratio of 3 to 4 , Start fraction 3 over 4 end fraction 4 to 3, 3:4, 43

The ratio comparing 4 electronic devices for every 3 people can be expressed in the following three ways:

  1. 4 to 3
  2. 4:3
  3. \(\frac{4}{3}\)

So, the correct response includes: 4 to 3, 4:3, \(\frac{4}{3}\).

How do you write 5 is to 1 as 20 is to 4 as a proportion in fractional notation?(1 point) Responses 5:1 :: 20:4 ratio of 5 to 1 colon colon ratio of 20 to 4 54=120 start fraction 5 over 4 end fraction equals start fraction 1 over 20 end fraction 51=420 start fraction 5 over 1 end fraction equals start fraction 4 over 20 end fraction 51=204

To write "5 is to 1 as 20 is to 4" as a proportion in fractional notation, you can use the following form:

\[ \frac{5}{1} = \frac{20}{4} \]

So the correct response includes: \(\frac{5}{1} = \frac{20}{4}\). However, based on the provided options, it sounds like you may need to indicate it using the form "5:1 :: 20:4," which expresses the same relationship.

Therefore, the correct answer from the options you provided would be: 5:1 :: 20:4.

You fill your car with 15 gallons of gas at a cost of $45. Using fractional notation, how do you write a proportion that shows how much 5 gallons of gas will cost? Use x to represent the unknown cost.(1 point) Responses 1545=5x Start Fraction 15 over 45 End Fraction equals Start Fraction 5 over x End Fraction 1545=x5 Start Fraction 15 over 45 End Fraction equals Start Fraction x over 5 End Fraction 15:45::x:5 ratio of 15 to 45 colon colon ratio of x to 5 15x=455

To write a proportion in fractional notation that shows how much 5 gallons of gas will cost using \(x\) to represent the unknown cost, you can set it up as follows:

\[ \frac{15}{45} = \frac{5}{x} \]

Therefore, the correct response from the provided options is: Start Fraction 15 over 45 End Fraction equals Start Fraction 5 over x End Fraction.