Question

(x+1)++(x+4)+(x+7)+...+(x+28)=156

Answer 1

\(\left(x+1\right)+\left(x+4\right)+\left(x+7\right)+...+\left(x+28\right)=156\)

\(\Leftrightarrow x+1+x+4+x+7+...+x+28=156\)

\(\Leftrightarrow\left(x+x+...+x\right)+\left(1+4+7+...+28\right)=156\)

\(\Leftrightarrow10x+\frac{\left(1+28\right)10}{2}=156\)

\(\Leftrightarrow10x+145=156\)

\(\Leftrightarrow10x=11\)

\(\Leftrightarrow x=\frac{11}{10}\)

Answer 2

$\left(x+1\right)+\left(x+4\right)+\left(x+7\right)+...+\left(x+28\right)=156$

$\iff x+1+x+4+x+7+...+x+28=156$

$\iff \left(x+x+...+x\right)+\left(1+4+7+...+28\right)=156$

$\iff 10x+\frac{\left(1+28\right)10}{2}=156$

$\iff 10x+145=156$

$\iff 10x=11$

$\iff x=\frac{11}{10}$