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Solve for x ..

−5x=−30

31 answers

To solve the equation \(-5x = -30\), you can divide both sides by \(-5\):

\[ x = \frac{-30}{-5} \]

This simplifies to:

\[ x = 6 \]

Thus, the solution is \(x = 6\).

solve for x
12 − x/9 = 11

To solve the equation \( 12 - \frac{x}{9} = 11 \), follow these steps:

  1. Subtract 12 from both sides:

    \[ -\frac{x}{9} = 11 - 12 \] \[ -\frac{x}{9} = -1 \]

  2. Multiply both sides by \(-1\) to eliminate the negative sign:

    \[ \frac{x}{9} = 1 \]

  3. Multiply both sides by 9 to solve for \(x\):

    \[ x = 9 \cdot 1 \] \[ x = 9 \]

Thus, the solution is \( x = 9 \).

Solve for x .
−20=−5+3x

To solve the equation \(-20 = -5 + 3x\), follow these steps:

  1. Add 5 to both sides to isolate the term with \(x\):

    \[ -20 + 5 = 3x \] \[ -15 = 3x \]

  2. Divide both sides by 3 to solve for \(x\):

    \[ x = \frac{-15}{3} \] \[ x = -5 \]

Thus, the solution is \(x = -5\).

20=5−3/8x

To solve the equation \( 20 = 5 - \frac{3}{8}x \), follow these steps:

  1. Subtract 5 from both sides:

    \[ 20 - 5 = -\frac{3}{8}x \] \[ 15 = -\frac{3}{8}x \]

  2. Multiply both sides by \(-\frac{8}{3}\) to solve for \(x\):

    \[ x = 15 \times -\frac{8}{3} \]

  3. Simplify the right side:

    \[ x = -\frac{120}{3} \] \[ x = -40 \]

Thus, the solution is \( x = -40 \).

7(4x−15)=63 solve for x

To solve the equation \(7(4x - 15) = 63\), follow these steps:

  1. Distribute the 7 to both terms inside the parentheses:

    \[ 28x - 105 = 63 \]

  2. Add 105 to both sides to isolate the term with \(x\):

    \[ 28x - 105 + 105 = 63 + 105 \] \[ 28x = 168 \]

  3. Divide both sides by 28 to solve for \(x\):

    \[ x = \frac{168}{28} \] \[ x = 6 \]

Thus, the solution is \(x = 6\).

Solve for x : −2(3x−15)−25=35 .(1 point)

To solve the equation \(-2(3x - 15) - 25 = 35\), follow these steps:

  1. Distribute \(-2\) to both terms inside the parentheses:

    \[ -6x + 30 - 25 = 35 \]

    This simplifies to:

    \[ -6x + 5 = 35 \]

  2. Subtract 5 from both sides to isolate the term with \(x\):

    \[ -6x + 5 - 5 = 35 - 5 \] \[ -6x = 30 \]

  3. Divide both sides by \(-6\) to solve for \(x\):

    \[ x = \frac{30}{-6} \] \[ x = -5 \]

Thus, the solution is \(x = -5\).

Solve for x : 12x+5=10x−11 .(1 point)

To solve the equation \(12x + 5 = 10x - 11\), follow these steps:

  1. Subtract \(10x\) from both sides to get all the \(x\) terms on one side:

    \[ 12x - 10x + 5 = -11 \] \[ 2x + 5 = -11 \]

  2. Subtract 5 from both sides to isolate the \(x\) term:

    \[ 2x + 5 - 5 = -11 - 5 \] \[ 2x = -16 \]

  3. Divide both sides by 2 to solve for \(x\):

    \[ x = \frac{-16}{2} \] \[ x = -8 \]

Thus, the solution is \(x = -8\).

After riding on the bus, Tran walked 30 minutes to get to her friend’s house. Her total travel time was 4 times as long as the bus ride. What equation does this situation model? Use t for the time of the bus ride.(1 point)

Let \( t \) be the time of the bus ride in minutes. According to the information provided:

  • The walking time is 30 minutes.
  • The total travel time is the sum of the bus ride time and the walking time, which can be written as \( t + 30 \) minutes.
  • The total travel time is also described as 4 times the bus ride time, which can be expressed as \( 4t \).

Putting this together, we can set up the following equation:

\[ t + 30 = 4t \]

This equation models the situation described in the problem.

At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.(1 point)

Let \( x \) represent the number of days.

For the first song, which starts with 1,000 listens and gets 38 new listens each day, the equation for the total number of listens after \( x \) days can be expressed as:

\[ 1000 + 38x \]

For the second song, which starts with 900 listens and gets 40 new listens each day, the equation for the total number of listens after \( x \) days is:

\[ 900 + 40x \]

To find out when the two songs will have the same number of listens, we can set these two expressions equal to each other:

\[ 1000 + 38x = 900 + 40x \]

This equation models the situation where the listens for both songs are equal after \( x \) days.

An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.(1 point)

Let's define \( x \) as the number of visits to the ice skating rink.

For the first option, where you pay \( $10 \) per visit, the total cost can be expressed as:

\[ \text{Cost}_1 = 10x \]

For the second option, which is \( $32 \) per month plus \( $6 \) per visit, the total cost can be expressed as:

\[ \text{Cost}_2 = 32 + 6x \]

To find the number of visits at which the costs of the two options are equal, we can set the two cost expressions equal to each other:

\[ 10x = 32 + 6x \]

Now, we will solve for \( x \):

  1. Subtract \( 6x \) from both sides:

    \[ 10x - 6x = 32 \] \[ 4x = 32 \]

  2. Divide both sides by 4:

    \[ x = \frac{32}{4} \] \[ x = 8 \]

Thus, it would take 8 visits for the cost of the two plans to be equal.

At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point)
The songs will have the same number of listens after BLANK
days.

Let \( x \) be the number of days.

For the first song, which starts with 700 listens and gets 52 new listens each day, the equation for the total number of listens after \( x \) days can be expressed as:

\[ \text{Total listens for Song 1} = 700 + 52x \]

For the second song, which starts with 600 listens and gets 56 new listens each day, the equation for the total number of listens after \( x \) days is:

\[ \text{Total listens for Song 2} = 600 + 56x \]

To find out when the two songs will have the same number of listens, we can set these two expressions equal to each other:

\[ 700 + 52x = 600 + 56x \]

Now we will solve for \( x \):

  1. Subtract \( 52x \) from both sides:

    \[ 700 = 600 + 4x \]

  2. Subtract 600 from both sides:

    \[ 700 - 600 = 4x \] \[ 100 = 4x \]

  3. Divide both sides by 4:

    \[ x = \frac{100}{4} \] \[ x = 25 \]

Thus, the two songs will have the same number of listens after 25 days.

Which of the following equations has exactly one solution?(1 point)
Responses

−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8

−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8

−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3

3x−8=3x+8
3 x minus 8 equals 3 x plus 8

To determine which of the given equations has exactly one solution, let's analyze each one:

  1. Equation: \(-3x + 8 = -3x - 8\)

    • Rearranging gives \(8 = -8\), which is a contradiction.
    • No solutions.

  2. Equation: \(-3x - 8 = 3x - 8\)

    • Rearranging gives \(-3x - 3x = -8 + 8\), which simplifies to \(-6x = 0\).
    • Dividing gives \(x = 0\).
    • One solution.

  3. Equation: \(-8x + 3 = -8x + 3\)

    • This is true for all \(x\), as both sides are identical.
    • Infinitely many solutions.

  4. Equation: \(3x - 8 = 3x + 8\)

    • Rearranging gives \(-8 = 8\), which is a contradiction.
    • No solutions.

Conclusion

The equation \(-3x - 8 = 3x - 8\) has exactly one solution (\(x = 0\)).

Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x (1 point)

To solve the equation \(11x = 3(7x - 1) - 10x\), follow these steps:

  1. Distribute the \(3\) on the right side of the equation:

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

  2. Combine like terms on the right side:

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

  3. Subtract \(11x\) from both sides:

    \[ 11x - 11x = 11x - 11x - 3 \] \[ 0 = -3 \]

The equation \(0 = -3\) is a contradiction and indicates that there are no solutions.

Conclusion

The given equation has none solutions.

Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6(1 point)

To solve the equation \(5(2x + 2) - 4 = 2x + 6\), follow these steps:

  1. Distribute the 5 on the left side:

    \[ 5 \cdot 2x + 5 \cdot 2 - 4 = 2x + 6 \]

    This simplifies to:

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

    Further simplifying gives:

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

  2. Subtract \(2x\) from both sides to get all the \(x\) terms on one side:

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

    This simplifies to:

    \[ 8x + 6 = 6 \]

  3. Subtract 6 from both sides:

    \[ 8x + 6 - 6 = 6 - 6 \]

    This simplifies to:

    \[ 8x = 0 \]

  4. Divide both sides by 8 to solve for \(x\):

    \[ x = \frac{0}{8} \]

    Thus,

    \[ x = 0 \]

Conclusion

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

Let's solve the equation \(5x + 8 + x = 32\) step by step.

Step 1: Combine like terms

Combine the \(x\) terms on the left side of the equation:

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

This simplifies to:

\[ 6x + 8 = 32 \]

Step 2: Isolate the term with \(x\)

Subtract \(8\) from both sides to isolate the term with \(x\):

\[ 6x + 8 - 8 = 32 - 8 \]

This simplifies to:

\[ 6x = 24 \]

Step 3: Solve for \(x\)

Divide both sides by \(6\):

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

Thus:

\[ x = 4 \]

Step 4: Check the solution

To check the solution, substitute \(x = 4\) back into the original equation:

Original equation:

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

Substituting \(x = 4\):

\[ 5(4) + 8 + 4 = 32 \]

Calculating the left side:

\[ 20 + 8 + 4 = 32 \] \[ 32 = 32 \]

The left side equals the right side, confirming that the solution is correct.

Conclusion

The solution to the equation is \(x = 4\).

they are all correct!

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