Alright, let's solve each of the given equations step-by-step.
### First Equation:
[tex]\[
\frac{8x}{3} = \frac{56}{8}
\][/tex]
To solve this equation for [tex]\( x \)[/tex], we first simplify the right-hand side:
[tex]\[
\frac{56}{8} = 7
\][/tex]
So the equation becomes:
[tex]\[
\frac{8x}{3} = 7
\][/tex]
Next, we solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]. We can do this by multiplying both sides of the equation by 3:
[tex]\[
8x = 7 \cdot 3
\][/tex]
[tex]\[
8x = 21
\][/tex]
Now, we divide both sides by 8:
[tex]\[
x = \frac{21}{8}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
x = 2.625
\][/tex]
So, the solution for the first equation is:
[tex]\[
x = 2.625
\][/tex]
### Second Equation:
[tex]\[
5(-x + 3) + 3x + 5 = 22
\][/tex]
First, we'll distribute the 5 in the left-hand side:
[tex]\[
5(-x) + 5(3) + 3x + 5 = 22
\][/tex]
[tex]\[
-5x + 15 + 3x + 5 = 22
\][/tex]
Next, we combine like terms:
[tex]\[
-5x + 3x + 20 = 22
\][/tex]
[tex]\[
-2x + 20 = 22
\][/tex]
To isolate [tex]\( x \)[/tex], we first subtract 20 from both sides:
[tex]\[
-2x = 22 - 20
\][/tex]
[tex]\[
-2x = 2
\][/tex]
Finally, we divide both sides by -2:
[tex]\[
x = \frac{2}{-2}
\][/tex]
[tex]\[
x = -1
\][/tex]
So, the solution for the second equation is:
[tex]\[
x = -1
\][/tex]
### Summary of Solutions:
For the first equation [tex]\(\frac{8x}{3} = \frac{56}{8}\)[/tex], the solution is:
[tex]\[
x = 2.625
\][/tex]
For the second equation [tex]\(5(-x + 3) + 3x + 5 = 22\)[/tex], the solution is:
[tex]\[
x = -1
\][/tex]
