Depict the wire information in a drawing. Draw a picture of the wire, and label its length "20 feet." Draw the 'cut' in the wire, making one piece larger than the other. Make a guess for how long the shorter piece is. It should be a number between 0 feet and 20 feet, not including 0 feet and 20 feet or the piece would be longer than the entire wire.. It does not matter if the guess is right or wrong. The guess will be used to form the equation. For this example, the number 5 will be used for the guess.
Complete the equation for the wire, using the number that was guessed. The larger piece is three more than twice the length of the smaller piece, or 3+2(smaller piece). If the smaller piece is 5 feet, then the longer piece is [3+2(5)] feet. The total length of the wire is: 5, (the shorter piece) + [3+2(5)], (the longer piece) = 20, (the total length). To see if the guess was correct, solve the equation. Begin with 2 multiplied by 5 is 10. Is 5+3+10=20? When these numbers are added together, the answer is 18=20. Because 18 does not equal 20, the guess is wrong.
Revise the equation. Write the same equation, 5+[3+2(5)]=20, but cross out the wrong guess, 5, with an X, which creates the equation X+3+2(X)=20. That inserts a variable into the equation in place of the unknown length of the shorter piece. X is the length of the shorter piece. Now that the equation has a variable, it can be solved for the variable, X. Students usually have difficulty creating an equation with a variable. Now that it is created, it takes only simple algebra to solve.
Solve the equation X+3+2(X)=20. Start by collecting like terms and isolate the X. The equivalent equation is [X+2X]+3=20. By combining like terms, the equation becomes 3X+3=20. To isolate the variable X, subtract the constant 3 from both sides, and then divide both sides by 3, the coefficient of X. This is equal to X=[20-3]/3, or X=17/3 or about 5.7. This is the length of the shorter piece. To find the length of the longer piece, use the equation for the longer piece, 3+2(X), to get 3+2(5.7)=3+11.4, which gives the approximate final length of the longer piece, 14.4. This answer is an approximation because the shorter piece is 17/3, which is equal to 5 2/3, and the longer piece is 43/3, which is 14 1/3. These fractions cannot be accurately expressed as decimals because they are repeating decimals. To get an exact answer, fractions must be used.