Sure, let's solve the equation:
[tex]\[
\frac{5(2x - 10)}{2} + 14 = 19
\][/tex]
Here’s the step-by-step solution:
1. Isolate the fraction term:
Subtract 14 from both sides of the equation to begin isolating the term that includes [tex]\( x \)[/tex].
[tex]\[
\frac{5(2x - 10)}{2} + 14 - 14 = 19 - 14
\][/tex]
[tex]\[
\frac{5(2x - 10)}{2} = 5
\][/tex]
2. Clear the fraction:
Multiply both sides of the equation by 2 to clear the fraction.
[tex]\[
2 \cdot \frac{5(2x - 10)}{2} = 2 \cdot 5
\][/tex]
[tex]\[
5(2x - 10) = 10
\][/tex]
3. Distribute the 5:
Distribute the 5 across the terms inside the parentheses.
[tex]\[
5 \cdot 2x - 5 \cdot 10 = 10
\][/tex]
[tex]\[
10x - 50 = 10
\][/tex]
4. Isolate the term with [tex]\( x \)[/tex]:
Add 50 to both sides of the equation to isolate the term with [tex]\( x \)[/tex].
[tex]\[
10x - 50 + 50 = 10 + 50
\][/tex]
[tex]\[
10x = 60
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
Divide both sides by 10 to solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{60}{10}
\][/tex]
[tex]\[
x = 6
\][/tex]
Thus, the solution to the equation is:
[tex]\[
x = 6
\][/tex]
