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Create and solve a single-variable equation with at least ten
terms. Five of the terms must be variable terms, the other five must be
constant terms. At least one of each of the variable terms must have a
fractional coefficient, a non-integer decimal coefficient, and a negative
coefficient. At least one of each of the constant terms must be a
fraction, a non-integer decimal, and a negative. You must use the
distributive property at least twice. The equation must start with five
terms on each side of the equation, with three variable terms on one side and
two on the other, and three constant terms on one side and two on the other
side. All coefficients and constants must be numerically distinct. Give an
exact answer, not a rounded decimal.

Answer :

MRROYALGO

The single-variable equation with at least ten terms is 7x  - 0.5x + 1/2x + 27 + 29 = 17x - x + 10 - 3 + 9, and the solution is x = 5

How to create the single variable equation?

Let the variable of the equation be x.

The rules in the question are:

  • The number of terms is 10;
  • At least one variable term must have a fractional coefficient
  • At least one variable term must be non integer decimal coefficient
  • At least one variable term must be negative

So, the equation must take the form

ax + bx + cx + f + g = dx + ex + h + i + j +k

So, we have:

7x  - 0.5x + 1/2x + 27 + 29 = 17x - x + 10 - 3 + 9

Evaluate the constant terms

7x  - 0.5x + 1/2x + 56 = 17x - x + 16

Evaluate the variable terms

8x  + 56 = 16x + 16

Apply the distributive property

8(x  + 7) = 16(x + 1)

Divide through by 4

2(x  + 7) = 4(x + 1)

Expand

2x + 14 = 4x + 4

Apply the distributive property

2(x  + 7) = 4(x + 1)

Divide through by 2

x + 7 = 2(x + 1)

Expand

x + 7 = 2x + 2

Collect like terms

2x - x = 7 - 2

Evaluate

x = 5

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