13x+7=8x+27

2x-1=7x+44

Step-by-step explanation:

1. Locate the x-term with the smallest coefficient. Identify the constant on the other side of the equation. Subtract the sum of those values from both sides of the equation:

  13x +7 -(7+8x) = 8x +27 -(7+8x)

  5x = 20 . . . . simplify

  x = 4 . . . . . . . divide by the coefficient of x

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2. Same procedure:

  2x -1 -(2x+44) = 7x +44 -(2x+44)

  -45 = 5x . . . . . . simplify

  -9 = x . . . . . . . . . divide by the coefficient of x

Comment on this type of problem

This sort of equation with constants and variables on both sides is called a 3-step linear equation, because it usually takes 3 steps to solve it:

In the above procedure, we have combined the first two steps. By locating and subtracting the variable term with the smallest coefficient, we ensure that the equation will have a positive coefficient for the variable. This can help reduce mistakes.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: