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Math  /  Algebra

QuestionQuestion 5
Solve the equation analytically. 0.01x+2.01=2.07x−0.050.01 x+2.01=2.07 x-0.05
The solution set of this equation is □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. The equation 0.01x+2.01=2.07x−0.05 0.01x + 2.01 = 2.07x - 0.05 is a linear equation.
2. The goal is to solve for x x .
3. The solution involves basic algebraic operations, including combining like terms and isolating the variable.

STEP 2

1. Move all terms involving x x to one side of the equation.
2. Move constant terms to the opposite side of the equation.
3. Solve for x x by isolating it.
4. Simplify the solution.

STEP 3

Subtract 0.01x 0.01x from both sides of the equation to move all terms involving x x to one side:
0.01x+2.01−0.01x=2.07x−0.05−0.01x 0.01x + 2.01 - 0.01x = 2.07x - 0.05 - 0.01x
This simplifies to:
2.01=2.06x−0.05 2.01 = 2.06x - 0.05

STEP 4

Add 0.05 0.05 to both sides of the equation to move constant terms to the opposite side:
2.01+0.05=2.06x−0.05+0.05 2.01 + 0.05 = 2.06x - 0.05 + 0.05
This simplifies to:
2.06=2.06x 2.06 = 2.06x

STEP 5

Divide both sides by 2.06 2.06 to solve for x x :
2.062.06=2.06x2.06 \frac{2.06}{2.06} = \frac{2.06x}{2.06}
This simplifies to:
x=1 x = 1

STEP 6

The solution set of the equation is:
1 \boxed{1}

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