3m + 5/4 - 3m/4=-2

7 answers

To solve the equation \( 3m + \frac{5}{4} - \frac{3m}{4} = -2 \), we first need to combine like terms. Let's start by rewriting the equation:

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

Next, we can combine the terms with \( m \). We can express \( 3m \) as \( \frac{12m}{4} \) to have a common denominator:

\[ \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4} \]

So, we can rewrite the equation:

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

To eliminate the fractions, let's multiply the entire equation by 4:

\[ 9m + 5 = -8 \]

Next, we will isolate \( 9m \) by subtracting 5 from both sides:

\[ 9m = -8 - 5 \]

This simplifies to:

\[ 9m = -13 \]

Now, divide both sides by 9:

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

Thus, the solution to the equation is:

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

w/2 - 7=11

To solve the equation

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

we'll start by isolating the term with \( w \). First, add 7 to both sides of the equation:

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

This simplifies to:

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

Next, multiply both sides by 2 to solve for \( w \):

\[ w = 18 \times 2. \]

This gives us:

\[ w = 36. \]

Thus, the solution to the equation is

\[ w = 36. \]

3b/15=1

To solve the equation

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

we can start by simplifying the left side. The fraction \(\frac{3}{15}\) simplifies to \(\frac{1}{5}\):

\[ \frac{3b}{15} = \frac{1}{5}. \]

So the equation can be rewritten as:

\[ \frac{1}{5}b = 1. \]

Next, multiply both sides of the equation by 5 to isolate \( b \):

\[ b = 1 \times 5. \]

This gives us:

\[ b = 5. \]

Thus, the solution to the equation is

\[ b = 5. \]

p/2+4=10

To solve the equation

\[ \frac{p}{2} + 4 = 10, \]

we start by isolating the term with \( p \). First, subtract 4 from both sides:

\[ \frac{p}{2} = 10 - 4. \]

This simplifies to:

\[ \frac{p}{2} = 6. \]

Next, to eliminate the fraction, multiply both sides by 2:

\[ p = 6 \times 2. \]

This gives us:

\[ p = 12. \]

Thus, the solution to the equation is

\[ p = 12. \]