Question
Solve for x in simplest form.
15, equals, start fraction, 3, divided by, 4, end fraction, left parenthesis, 5, x, plus, 8, right parenthesis
15=
4
3
(5x+8)
15, equals, start fraction, 3, divided by, 4, end fraction, left parenthesis, 5, x, plus, 8, right parenthesis
15=
4
3
(5x+8)
Answers
Answered by
GPT-4o mini
To solve for \( x \) in the equation
\[
15 = \frac{3}{4}(5x + 8),
\]
we'll begin by eliminating the fraction. To do this, we can multiply both sides of the equation by 4:
\[
4 \cdot 15 = 4 \cdot \frac{3}{4}(5x + 8).
\]
This simplifies to:
\[
60 = 3(5x + 8).
\]
Next, distribute the 3 on the right side:
\[
60 = 15x + 24.
\]
Now, we want to isolate \( x \). Start by subtracting 24 from both sides:
\[
60 - 24 = 15x,
\]
which simplifies to:
\[
36 = 15x.
\]
Next, divide both sides by 15:
\[
x = \frac{36}{15}.
\]
We can simplify the fraction by finding the greatest common divisor (GCD) of 36 and 15, which is 3:
\[
x = \frac{36 \div 3}{15 \div 3} = \frac{12}{5}.
\]
Thus, the solution for \( x \) in simplest form is
\[
\boxed{\frac{12}{5}}.
\]
\[
15 = \frac{3}{4}(5x + 8),
\]
we'll begin by eliminating the fraction. To do this, we can multiply both sides of the equation by 4:
\[
4 \cdot 15 = 4 \cdot \frac{3}{4}(5x + 8).
\]
This simplifies to:
\[
60 = 3(5x + 8).
\]
Next, distribute the 3 on the right side:
\[
60 = 15x + 24.
\]
Now, we want to isolate \( x \). Start by subtracting 24 from both sides:
\[
60 - 24 = 15x,
\]
which simplifies to:
\[
36 = 15x.
\]
Next, divide both sides by 15:
\[
x = \frac{36}{15}.
\]
We can simplify the fraction by finding the greatest common divisor (GCD) of 36 and 15, which is 3:
\[
x = \frac{36 \div 3}{15 \div 3} = \frac{12}{5}.
\]
Thus, the solution for \( x \) in simplest form is
\[
\boxed{\frac{12}{5}}.
\]