Math  /  Algebra

QuestionSolve. 0.5x2.8=0.70.5 x-2.8=0.7
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=x= \square (Simplify your answer.) B. The solution is all real numbers. C. There is no solution.

Studdy Solution

STEP 1

1. The equation 0.5x2.8=0.7 0.5x - 2.8 = 0.7 is a linear equation in one variable.
2. We are solving for x x .
3. The equation involves basic algebraic operations, specifically addition and division.

STEP 2

1. Isolate the term containing x x .
2. Solve for x x by performing algebraic operations.
3. Verify the solution by substituting it back into the original equation.
4. Determine the correct choice from the given options.

STEP 3

To isolate the term containing x x , add 2.8 2.8 to both sides of the equation:
0.5x2.8+2.8=0.7+2.8 0.5x - 2.8 + 2.8 = 0.7 + 2.8
This simplifies to:
0.5x=3.5 0.5x = 3.5

STEP 4

Now, solve for x x by dividing both sides by 0.5 0.5 :
0.5x0.5=3.50.5 \frac{0.5x}{0.5} = \frac{3.5}{0.5}
This simplifies to:
x=7 x = 7

STEP 5

Verify the solution by substituting x=7 x = 7 back into the original equation:
0.5(7)2.8=0.7 0.5(7) - 2.8 = 0.7
Calculate the left-hand side:
3.52.8=0.7 3.5 - 2.8 = 0.7
Since both sides are equal, the solution is verified.

STEP 6

Determine the correct choice from the given options:
A. x=7 x = 7 (Simplify your answer.) B. The solution is all real numbers. C. There is no solution.
The correct choice is:
A. x=7 x = 7

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