Given:
two-thirds a number plus 4 is 7
First Part: Converting the statement into equation
Let x be the number in the given statement.
The phrase "two-thirds a number" can be expressed as
[tex]\frac{2}{3}x[/tex]Pair it with "... plus 4" and we get
[tex]\frac{2}{3}x+4[/tex]Finally, it is stated it is equal to 7, and we complete the equation
[tex]\frac{2}{3}x+4=7[/tex]Second Part: Solving for the number
Now, that we have the equation, we can now solve for the missing number x.
Subtract both sides by 4, to remove the constant 4 on the left side of the equation
[tex]\begin{gathered} \frac{2}{3}x+4=7 \\ \frac{2}{3}x+4-4=7-4 \\ \frac{2}{3}x\cancel{+4-4}=3 \\ \frac{2}{3}x=3 \end{gathered}[/tex]Multiply both sides by 3/2, and we get
[tex]\begin{gathered} \frac{2}{3}x=3 \\ \frac{2}{3}x\cdot\frac{3}{2}=3\cdot\frac{3}{2} \\ \frac{\cancel{2}}{\cancel{3}}x\cdot\frac{\cancel{3}}{\cancel{2}}=\frac{9}{2} \\ x=\frac{9}{2} \end{gathered}[/tex]Therefore, the number is 9/2 or nine-halves.
