Sure, let's solve the equation [tex]\(\frac{x+8}{3} = \frac{3x-2}{8}\)[/tex] using cross multiplication.
1. Cross Multiply: To solve the equation, we start by cross-multiplying to get rid of the fractions. This means we'll multiply the numerator of the left fraction by the denominator of the right fraction and set it equal to the denominator of the left fraction multiplied by the numerator of the right fraction:
[tex]\[
(x + 8) \times 8 = (3x - 2) \times 3
\][/tex]
2. Distribute: Next, we distribute the constants across the parentheses:
[tex]\[
8(x + 8) = 3(3x - 2)
\][/tex]
Which simplifies to:
[tex]\[
8x + 64 = 9x - 6
\][/tex]
3. Simplify the Equation: Now we need to combine like terms. First, we'll move all the [tex]\(x\)[/tex] terms to one side of the equation and constants to the other side:
[tex]\[
8x + 64 = 9x - 6
\][/tex]
[tex]\[
64 + 6 = 9x - 8x
\][/tex]
[tex]\[
70 = x
\][/tex]
4. Solution: Therefore, the value of [tex]\(x\)[/tex] that satisfies the given equation is:
[tex]\[
x = 70
\][/tex]
So, the solution to the equation [tex]\(\frac{x+8}{3} = \frac{3x-2}{8}\)[/tex] using cross multiplication is:
[tex]\[
x = 70
\][/tex]
