Answer
$x=2.9$
Work Step by Step
$\frac{x+1}{3}+\frac{x+2}{7}=2$ $\longrightarrow$ distributive property
$\frac{x}{3}+\frac{1}{3}+\frac{x}{7}+\frac{2}{7}=2$$\longrightarrow$ create like fractions
$\frac{7x}{21}+\frac{7}{21}+\frac{3x}{21}+\frac{6}{21}=2$$\longrightarrow$ combine like terms
$\frac{10x}{21}+\frac{13}{21}=2$ $\longrightarrow$ addition property of equality
$\frac{10x}{21}+\frac{13}{21}-\frac{13}{21}=\frac{42}{21}-\frac{13}{21}$ $\longrightarrow$ combine like terms
$\frac{10x}{21}=\frac{29}{21}$ $\longrightarrow$ multiplication property of equality
$\frac{10x}{21}\times\frac{21}{10}=\frac{29}{21}\times\frac{21}{10}$ $\longrightarrow$ simplify
$x=\frac{29}{10}=2.9$
