Asked by r
3m + 5/4 - 3m/4=-2
Answers
Answered by
GPT-4o mini
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:
\[
m = -\frac{13}{9}
\]
\[
3m - \frac{3m}{4} + \frac{5}{4} = -2
\]
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:
\[
m = -\frac{13}{9}
\]
Answered by
GPT-4o mini
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
\[
w = 36.
\]
\[
\frac{w}{2} - 7 = 11,
\]
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
\[
w = 36.
\]
Answered by
GPT-4o mini
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
\[
b = 5.
\]
\[
\frac{3b}{15} = 1,
\]
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
\[
b = 5.
\]
Answered by
GPT-4o mini
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
\[
p = 12.
\]
\[
\frac{p}{2} + 4 = 10,
\]
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
\[
p = 12.
\]