Solve each equation using simplification techniques. Round answer to two decimal places as necessary.
[tex]$-34 x-93=36 x+49$[/tex]
Answer (2)
Add 34 x to both sides: − 93 = 70 x + 49 .
Subtract 49 from both sides: − 142 = 70 x .
Divide both sides by 70: x = − 70 142 .
Simplify and round to two decimal places: x ≈ − 2.03 .
Explanation
Understanding the Problem We are given the equation − 34 x − 93 = 36 x + 49 and asked to solve for x , rounding the answer to two decimal places.
Adding 34x to Both Sides First, we want to isolate the terms with x on one side of the equation and the constant terms on the other side. To do this, we can add 34 x to both sides of the equation: − 34 x − 93 + 34 x = 36 x + 49 + 34 x which simplifies to − 93 = 70 x + 49.
Subtracting 49 from Both Sides Next, we subtract 49 from both sides of the equation to isolate the term with x :
− 93 − 49 = 70 x + 49 − 49 which simplifies to − 142 = 70 x .
Dividing by 70 Now, we divide both sides by 70 to solve for x :
70 − 142 = 70 70 x which simplifies to x = − 70 142 .
Simplifying the Fraction We can simplify the fraction by dividing both the numerator and the denominator by 2: x = − 35 71 .
Converting to Decimal and Rounding To convert this fraction to a decimal, we divide -71 by 35, which gives us approximately -2.02857. Rounding to two decimal places, we get x ≈ − 2.03 .
Final Answer Therefore, the solution to the equation, rounded to two decimal places, is x ≈ − 2.03 .
Examples
Imagine you're comparing phone plans. Plan A costs $93 upfront plus $34 per month, while Plan B costs $49 upfront plus 36 p er m o n t h . S o l v in g t h ee q u a t i o n -34x - 93 = 36x + 49$ helps you determine after how many months the total cost of both plans would be the same. This type of problem is useful for making informed decisions when comparing costs over time.
By following the steps of isolating the variable, we find that the solution to the equation is approximately x ≈ − 2.03 . This result is obtained through algebraic manipulation and rounding to two decimal places. Ultimately, we successfully isolate x through a series of additive and subtractive transformations.
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