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What value will make the equation 3m+5/4−3m/4=−2 true? Write your answer as a fraction.(1 point)

The value for m that makes the equation true is m=()

7 answers

To solve the equation \( 3m + \frac{5}{4} - \frac{3m}{4} = -2 \), we can start by combining like terms.

First, we can express \( 3m \) as a fraction with a denominator of 4:

\[ 3m = \frac{12m}{4} \]

Now, substitute this into the equation:

\[ \frac{12m}{4} + \frac{5}{4} - \frac{3m}{4} = -2 \]

Next, combine the terms on the left side:

\[ \frac{12m - 3m + 5}{4} = -2 \]

This simplifies to:

\[ \frac{9m + 5}{4} = -2 \]

Next, we eliminate the fraction by multiplying both sides by 4:

\[ 9m + 5 = -8 \]

Now, isolate \( 9m \) by subtracting 5 from both sides:

\[ 9m = -8 - 5 \] \[ 9m = -13 \]

Finally, divide by 9 to solve for \( m \):

\[ m = \frac{-13}{9} \]

Thus, the value for \( m \) that makes the equation true is:

\[ m = \frac{-13}{9} \]

Using the properties of equality, solve the equation 1/4(8−16g)+8=g .(1 point)

The solution to the equation is g=()

To solve the equation

\[ \frac{1}{4}(8 - 16g) + 8 = g, \]

we will use the properties of equality step by step.

  1. Distribute the \(\frac{1}{4}\):

\[ \frac{1}{4} \cdot 8 - \frac{1}{4} \cdot 16g + 8 = g \]

This simplifies to:

\[ 2 - 4g + 8 = g \]

  1. Combine like terms on the left side:

\[ 10 - 4g = g \]

  1. Add \(4g\) to both sides to get all \(g\) terms on one side:

\[ 10 = g + 4g \]

This simplifies to:

\[ 10 = 5g \]

  1. Divide both sides by 5:

\[ g = \frac{10}{5} \]

This simplifies to:

\[ g = 2 \]

Thus, the solution to the equation is:

\[ g = 2 \]

Sehyr solved the equation w/2−7=11 . She seems to have made an error in her work because the solution she found does not work. Observe Sehyr’s work to find her error and correct it to find the solution to the equation.
Sehyr’s work: w/2−7=11
w/2−7+7=11+7 Using the Addition Property of Equality
w/2/2=18/2 Using the Division Property of Equality w=9 (1 point)

The solution to the equation is ()

Let's analyze Sehyr's work step by step and find where she made an error.

  1. Original Equation:

    \[ \frac{w}{2} - 7 = 11 \]

  2. Add 7 to both sides (correct application of the Addition Property of Equality):

    \[ \frac{w}{2} - 7 + 7 = 11 + 7 \]

    This simplifies correctly to:

    \[ \frac{w}{2} = 18 \]

  3. Next step: Sehyr incorrectly wrote:

    \[ \frac{w}{2}/2 = \frac{18}{2} \]

    The correct next step is to multiply both sides by 2 (instead of dividing):

    \[ w = 18 \times 2 \]

    This gives:

    \[ w = 36 \]

In summary, Sehyr made an error when she used the Division Property of Equality instead of multiplying both sides by 2.

Thus, the correct solution to the equation is:

\[ w = 36 \]

How many of the following equations have the solution set {5} ? 2(x−3)+1=5 3b/15=1 2h−30=40 (1 point)

The number of equations that have the solution set {5} is ()

Let's solve each given equation to determine how many of them have the solution \( {5} \).

  1. Equation 1:

    \[ 2(x - 3) + 1 = 5 \]

    First, distribute the 2:

    \[ 2x - 6 + 1 = 5 \]

    Simplifying this gives:

    \[ 2x - 5 = 5 \]

    Next, add 5 to both sides:

    \[ 2x = 10 \]

    Now, divide by 2:

    \[ x = 5 \]

    So, this equation has the solution 5.

  2. Equation 2:

    \[ \frac{3b}{15} = 1 \]

    Multiply both sides by 15:

    \[ 3b = 15 \]

    Now, divide by 3:

    \[ b = 5 \]

    This equation also has the solution 5.

  3. Equation 3:

    \[ 2h - 30 = 40 \]

    Add 30 to both sides:

    \[ 2h = 70 \]

    Now, divide by 2:

    \[ h = 35 \]

    This equation does not have the solution 5.

Now, we can summarize:

  • Equation 1 has the solution set \({5}\).
  • Equation 2 has the solution set \({5}\).
  • Equation 3 does not have the solution 5.

Therefore, the number of equations that have the solution set \({5}\) is:

\[ \text{2} \]