Let's solve the equation \(2 = \frac{7}{2}(5x + 6)\) step by step:
1. Eliminate the Fraction:
To get rid of the fraction, multiply both sides of the equation by 2:
[tex]\[
2 \cdot 2 = \frac{7}{2}(5x + 6) \cdot 2
\][/tex]
[tex]\[
4 = 7(5x + 6)
\][/tex]
2. Distribute the 7 on the Right Side:
Now, distribute the 7 through the parentheses on the right side:
[tex]\[
4 = 7 \cdot 5x + 7 \cdot 6
\][/tex]
[tex]\[
4 = 35x + 42
\][/tex]
3. Isolate the Term Involving \(x\):
Subtract 42 from both sides to isolate the term involving \(x\):
[tex]\[
4 - 42 = 35x
\][/tex]
[tex]\[
-38 = 35x
\][/tex]
4. Solve for \(x\):
Finally, divide both sides of the equation by 35 to solve for \(x\):
[tex]\[
x = \frac{-38}{35}
\][/tex]
5. Simplify the Fraction:
The fraction \(\frac{-38}{35}\) is in its simplest form because the numerator and the denominator have no common factors other than 1. As an approximate decimal value:
[tex]\[
x \approx -1.0857142857142856
\][/tex]
So, the solution to the equation \(2 = \frac{7}{2}(5x + 6)\) is:
[tex]\[
x = \frac{-38}{35} \approx -1.0857142857142856
\][/tex]
