QuestionA Thanksgiving sweater is knitted with $2(x+5)+3(2 x-4)=19$ of yarn. Find $x$.

Studdy Solution
Check the solution by substituting $x = \frac{21}{8}$ back into the original equation:
$$2\left(\frac{21}{8} + 5\right) + 3\left(2\left(\frac{21}{8}\right) - 4\right) = 19$$
Calculate each part:
$$2\left(\frac{21}{8} + \frac{40}{8}\right) = 2\left(\frac{61}{8}\right) = \frac{122}{8} = 15.25$$
$$3\left(\frac{42}{8} - \frac{32}{8}\right) = 3\left(\frac{10}{8}\right) = \frac{30}{8} = 3.75$$
Add them together:
$$15.25 + 3.75 = 19$$
Both sides are equal, confirming the solution is correct.
The solution is:
$$\boxed{\frac{21}{8}}$$