[tex]Solution; \\ Let\ x\ be\ the\ smallest\ even\ number. \\ Let\ x+2\ be\ the\ next\ even\ number. \\ Let\ x+4\ be\ the\ next\ even\ number. \\ Let\ x+6\ be\ the\ next\ even\ number. \\ Let\ x+8\ be\ the\ next\ even\ number. \\ Let\ x+10\ be\ the\ next\ even\ number;and \\ Let\ x+12\ be\ the\ biggest\ even\ number. \\ \\ Equation; \\ \\ \frac{x+x+2+x+4+x+6+x+8+x+10+x+12}{7}=42 \\ \\ \frac{7x+42}{7}=42 \\ \\ x+6=42 \\ \\ x=42-6 \\ \\ \boxed{\boxed{x=36}} [/tex]
[tex]Conclusion; \\ Thus,\underline{36}\ is\ the\ smallest\ even\ number. \\ \\ Checking; \\ Where\ x\to36 \\ \\ x\to36 \\ x+2\to38 \\ x+4\to40 \\ x+6\to42 \\ x+8\to44 \\ x+10\to46 \\ x+12\to48 \\ \\ \frac{36+38+40+42+44+46+48}{7}=42 \\ \\ \frac{294}{7}=42 \\ \\ \boxed{\boxed{42=42}}\ \underline{TRUE} \\ \\ Hope\ it\ Helps:) \\ Domini [/tex]
