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Math  /  Algebra

QuestionDetermine the number of solutions for the following linear equation: 28x−16=4(7x−4)28 x-16=4(7 x-4) No Solution Infinitely Many Solutions One Solution

Studdy Solution

STEP 1

1. We are dealing with a linear equation of the form ax+b=cx+d ax + b = cx + d .
2. The equation can have no solution, one solution, or infinitely many solutions.
3. We will solve the equation to determine the number of solutions.

STEP 2

1. Simplify both sides of the equation.
2. Compare coefficients of x x and constant terms.
3. Determine the number of solutions based on the comparison.

STEP 3

Simplify both sides of the equation:
The given equation is:
28x−16=4(7x−4) 28x - 16 = 4(7x - 4)
First, distribute the 4 on the right side:
4(7x−4)=28x−16 4(7x - 4) = 28x - 16
So, the equation becomes:
28x−16=28x−16 28x - 16 = 28x - 16

STEP 4

Compare coefficients of x x and constant terms:
The equation 28x−16=28x−16 28x - 16 = 28x - 16 has the same coefficients for x x and the same constant terms on both sides.

STEP 5

Determine the number of solutions:
Since both sides of the equation are identical, this means the equation is true for all values of x x . Therefore, there are infinitely many solutions.
The number of solutions is: Infinitely Many Solutions.

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