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3 years ago

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Rahul solved the equation 2(x – ) – 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartF

raction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction x = 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction . In which step did he use the addition property of equality?

2 answers:

Archy [21]3 years ago

6 0

Answer:

step 2

Step-by-step

the other guy said it.

Ghella [55]3 years ago

3 0

Rahul use addition property of equality in step 2.

Solution:

The image of the question is attached below.

Step 1:

$$2 x-\frac{1}{4}-\frac{3}{5} x=\frac{55}{4}$

combine like terms together.

$$2 x-\frac{3}{5} x-\frac{1}{4}=\frac{55}{4}$

To make the denominator same multiply and divide 2x by 5.

$$\frac{10}{5} x-\frac{3}{5} x-\frac{1}{4}=\frac{55}{4}$

Step 2:

$$\frac{7}{5} x-\frac{1}{4}=\frac{55}{4}$

By addition property of equality, add $\frac{1}{4}$ on both side of the equation.

$$\frac{7}{5} x-\frac{1}{4}+\frac{1}{4}=\frac{55}{4}+\frac{1}{4}$

Step 3:

$$ \frac{7}{5} x=\frac{56}{4}$

Step 4:

Multiply by $\frac{5}{7}$ on both side of the equation.

$x=10$

Hence Rahul use addition property of equality in step 2.

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Read 2 more answers

Use Gaussian elimination to write each system in triangular form

Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is $x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

Swapping two rows
Multiplying a row by a nonzero number
Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

$\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]$

For this matrix we need to perform the following row operations:

$R_2 - 1 R_1 \rightarrow R_2$ (multiply 1 row by 1 and subtract it from 2 row)
$R_3 + 1 R_1 \rightarrow R_3$ (multiply 1 row by 1 and add it to 3 row)
$R_4 - 1 R_1 \rightarrow R_4$ (multiply 1 row by 1 and subtract it from 4 row)

$R_2 \leftrightarrow R_3$ (interchange the 2 and 3 rows)

$R_2 / 2 \rightarrow R_2$ (divide the 2 row by 2)
$R_1 - 1 R_2 \rightarrow R_1$ (multiply 2 row by 1 and subtract it from 1 row)
$R_4 - 1 R_2 \rightarrow R_4$ (multiply 2 row by 1 and subtract it from 4 row)
$R_3 \cdot ( -1) \rightarrow R_3$ (multiply the 3 row by -1)
$R_2 - 1 R_3 \rightarrow R_2$ (multiply 3 row by 1 and subtract it from 2 row)
$R_4 + 3 R_3 \rightarrow R_4$ (multiply 3 row by 3 and add it to 4 row)
$R_4 / 4.5 \rightarrow R_4$ (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5 \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 & 2 \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

If you later perform the following operations you can find the solution to the system.

$R_1 + 0.5 R_4 \rightarrow R_1$ (multiply 4 row by 0.5 and add it to 1 row)
$R_2 + 0.5 R_4 \rightarrow R_2$ (multiply 4 row by 0.5 and add it to 2 row)
$R_3 - 2 R_4 \rightarrow R_3$ (multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9} \\0 & 1 & 0 & 0 & -\frac{1}{9}\\0 & 0 & 1 & 0 & \frac{4}{9} \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

Thus, the solution is:

$x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

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