Sure! Let's solve the equation [tex]\(\frac{2}{3} x + 19 = 35\)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
\frac{2}{3} x + 19 = 35
\][/tex]
2. Isolate the term containing [tex]\(x\)[/tex] by subtracting 19 from both sides of the equation:
[tex]\[
\frac{2}{3} x + 19 - 19 = 35 - 19
\][/tex]
Simplifying the equation, we get:
[tex]\[
\frac{2}{3} x = 16
\][/tex]
3. Solve for [tex]\(x\)[/tex] by getting rid of the fraction. To do this, multiply both sides of the equation by the reciprocal of [tex]\(\frac{2}{3}\)[/tex], which is [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\left(\frac{2}{3} x\right) \cdot \frac{3}{2} = 16 \cdot \frac{3}{2}
\][/tex]
4. Simplify the equation:
[tex]\[
x = 16 \cdot \frac{3}{2}
\][/tex]
Performing the multiplication on the right-hand side, we obtain:
[tex]\[
x = 24
\][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\frac{2}{3} x + 19 = 35\)[/tex] is [tex]\(x = 24\)[/tex].
