Get clear, concise, and accurate answers to your questions on IDNLearn.com. Our platform is designed to provide quick and accurate answers to any questions you may have.
Sagot :
To determine the step at which Rahul used the addition property of equality, let’s carefully examine each step of the solution in detail:
### Initial Equation
The original equation is:
[tex]\[ 2\left(x - \frac{1}{8}\right) - \frac{3}{5}x = \frac{55}{4} \][/tex]
### Step 1
In Step 1, Rahul expands and simplifies the expression:
[tex]\[ 2\left(x - \frac{1}{8}\right) - \frac{3}{5}x = \frac{55}{4} \][/tex]
Expanding:
[tex]\[ 2x - \frac{2}{8} - \frac{3}{5}x = \frac{55}{4} \][/tex]
Simplifying [tex]\(\frac{2}{8}\)[/tex] to [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ 2x - \frac{1}{4} - \frac{3}{5}x = \frac{55}{4} \][/tex]
### Step 2
Next, in Step 2, Rahul combines like terms:
[tex]\[ 2x - \frac{3}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
Converting [tex]\(2x\)[/tex] to [tex]\(\frac{10}{5}x\)[/tex]:
[tex]\[ \frac{10}{5}x - \frac{3}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
Combining [tex]\(\frac{10}{5}x\)[/tex] and [tex]\(\frac{3}{5}x\)[/tex]:
[tex]\[ \frac{7}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
### Step 3
In Step 3, Rahul isolates the term with [tex]\(x\)[/tex] by adding [tex]\(\frac{1}{4}\)[/tex] to both sides of the equation:
[tex]\[ \frac{7}{5}x - \frac{1}{4} + \frac{1}{4} = \frac{55}{4} + \frac{1}{4} \][/tex]
This simplifies to:
[tex]\[ \frac{7}{5}x = \frac{56}{4} \][/tex]
In this step, Rahul used the addition property of equality. This property states that adding the same number to both sides of an equation helps to isolate the variable without changing the equality.
### Step 4
Finally, in Step 4, Rahul solves for [tex]\(x\)[/tex]:
[tex]\[ \frac{7}{5}x = \frac{56}{4} \][/tex]
Simplifying [tex]\(\frac{56}{4}\)[/tex] to [tex]\(14\)[/tex]:
[tex]\[ \frac{7}{5}x = 14 \][/tex]
Multiplying both sides by [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[ x = 10 \][/tex]
### Conclusion
The addition property of equality was used in Step 3 when Rahul added [tex]\(\frac{1}{4}\)[/tex] to both sides of the equation.
### Initial Equation
The original equation is:
[tex]\[ 2\left(x - \frac{1}{8}\right) - \frac{3}{5}x = \frac{55}{4} \][/tex]
### Step 1
In Step 1, Rahul expands and simplifies the expression:
[tex]\[ 2\left(x - \frac{1}{8}\right) - \frac{3}{5}x = \frac{55}{4} \][/tex]
Expanding:
[tex]\[ 2x - \frac{2}{8} - \frac{3}{5}x = \frac{55}{4} \][/tex]
Simplifying [tex]\(\frac{2}{8}\)[/tex] to [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ 2x - \frac{1}{4} - \frac{3}{5}x = \frac{55}{4} \][/tex]
### Step 2
Next, in Step 2, Rahul combines like terms:
[tex]\[ 2x - \frac{3}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
Converting [tex]\(2x\)[/tex] to [tex]\(\frac{10}{5}x\)[/tex]:
[tex]\[ \frac{10}{5}x - \frac{3}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
Combining [tex]\(\frac{10}{5}x\)[/tex] and [tex]\(\frac{3}{5}x\)[/tex]:
[tex]\[ \frac{7}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
### Step 3
In Step 3, Rahul isolates the term with [tex]\(x\)[/tex] by adding [tex]\(\frac{1}{4}\)[/tex] to both sides of the equation:
[tex]\[ \frac{7}{5}x - \frac{1}{4} + \frac{1}{4} = \frac{55}{4} + \frac{1}{4} \][/tex]
This simplifies to:
[tex]\[ \frac{7}{5}x = \frac{56}{4} \][/tex]
In this step, Rahul used the addition property of equality. This property states that adding the same number to both sides of an equation helps to isolate the variable without changing the equality.
### Step 4
Finally, in Step 4, Rahul solves for [tex]\(x\)[/tex]:
[tex]\[ \frac{7}{5}x = \frac{56}{4} \][/tex]
Simplifying [tex]\(\frac{56}{4}\)[/tex] to [tex]\(14\)[/tex]:
[tex]\[ \frac{7}{5}x = 14 \][/tex]
Multiplying both sides by [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[ x = 10 \][/tex]
### Conclusion
The addition property of equality was used in Step 3 when Rahul added [tex]\(\frac{1}{4}\)[/tex] to both sides of the equation.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.
