Question

solve the equation.
0.5x + \frac{8}{5}x = x + 11
the solution set is \\{\\ \\}. (simplify your answer.)

Explanation:

Step1: Convert decimals to fractions

$0.5 = \frac{1}{2}$, so rewrite the equation:
$\frac{1}{2}x + \frac{8}{5}x = x + 11$

Step2: Combine left-side terms

Find common denominator 10:
$\frac{5}{10}x + \frac{16}{10}x = x + 11$
$\frac{21}{10}x = x + 11$

Step3: Isolate x terms

Subtract $x$ (or $\frac{10}{10}x$) from both sides:
$\frac{21}{10}x - \frac{10}{10}x = 11$
$\frac{11}{10}x = 11$

Step4: Solve for x

Multiply both sides by $\frac{10}{11}$:
$x = 11 \times \frac{10}{11}$

Answer:

$\{10\}$