Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Fill in the blanks.

1. [tex]$7x \qquad = 1$[/tex]
2. [tex]$\frac{2}{9}x \qquad = 2$[/tex]
3. [tex]$\frac{4}{7}x \qquad = 1$[/tex]
4. [tex]$\frac{17}{19}x \qquad = 1$[/tex]


Sagot :

Certainly! Let's solve each equation step-by-step to find the value of [tex]\( x \)[/tex] for each one.

1. [tex]\( 7x = 1 \)[/tex]

To solve for [tex]\( x \)[/tex], we divide both sides by 7:

[tex]\[ x = \frac{1}{7} \][/tex]

Therefore, [tex]\( x \)[/tex] in this case is:

[tex]\[ x = 0.14285714285714285 \][/tex]

2. [tex]\(\frac{2}{9}x = 2\)[/tex]

To solve for [tex]\( x \)[/tex] here, we need to multiply both sides by the reciprocal of [tex]\(\frac{2}{9}\)[/tex]:

[tex]\[ x = 2 \times \frac{9}{2} \][/tex]

[tex]\[ x = 9.0 \][/tex]

Therefore, [tex]\( x \)[/tex] in this case is:

[tex]\[ x = 9.0 \][/tex]

3. [tex]\(\frac{4}{7}x = 1\)[/tex]

To solve for [tex]\( x \)[/tex], we again multiply both sides by the reciprocal of [tex]\(\frac{4}{7}\)[/tex]:

[tex]\[ x = 1 \times \frac{7}{4} \][/tex]

[tex]\[ x = 1.75 \][/tex]

Therefore, [tex]\( x \)[/tex] in this case is:

[tex]\[ x = 1.75 \][/tex]

4. [tex]\(\frac{17}{19}x = 1\)[/tex]

Similarly, multiplying both sides by the reciprocal of [tex]\(\frac{17}{19}\)[/tex]:

[tex]\[ x = 1 \times \frac{19}{17} \][/tex]

[tex]\[ x = 1.1176470588235294 \][/tex]

Therefore, [tex]\( x \)[/tex] in this case is:

[tex]\[ x = 1.1176470588235294 \][/tex]

Thus, the completed equations with their solutions are:

1. [tex]\( 7x = 1 \)[/tex] ⟹ [tex]\( x = 0.14285714285714285 \)[/tex]
2. [tex]\(\frac{2}{9}x = 2\)[/tex] ⟹ [tex]\( x = 9.0 \)[/tex]
3. [tex]\(\frac{4}{7}x = 1\)[/tex] ⟹ [tex]\( x = 1.75 \)[/tex]
4. [tex]\(\frac{17}{19}x = 1\)[/tex] ⟹ [tex]\( x = 1.1176470588235294 \)[/tex]

Answer:To solve each equation and fill in the blanks:

1. \( 7x = 1 \)

  Solve for \( x \):

  \[

  x = \frac{1}{7}

  \]

  Therefore, \( 7x = 1 \) corresponds to \( x = \frac{1}{7} \).

2. \( \frac{2}{9}x = 2 \)

  Solve for \( x \):

  \[

  x = \frac{2 \cdot 9}{2} = 9

  \]

  Therefore, \( \frac{2}{9}x = 2 \) corresponds to \( x = 9 \).

3. \( \frac{4}{7}x = 1 \)

  Solve for \( x \):

  \[

  x = \frac{7}{4}

  \]

  Therefore, \( \frac{4}{7}x = 1 \) corresponds to \( x = \frac{7}{4} \).

4. \( \frac{17}{19}x = 1 \)

  Solve for \( x \):

  \[

  x = \frac{19}{17}

  \]

  Therefore, \( \frac{17}{19}x = 1 \) corresponds to \( x = \frac{19}{17} \).

### Filling in the Blanks:

1. \( 7x \quad = \frac{1}{7} \)

2. \( \frac{2}{9}x \quad = 9 \)

3. \( \frac{4}{7}x \quad = \frac{7}{4} \)

4. \( \frac{17}{19}x \quad = \frac{19}{17} \)

These are the filled-in blanks for each equation after solving for \( x \).

Step-by-step explanation:Certainly! Let's go through each equation step-by-step and solve for \( x \).

### 1. \( 7x = 1 \)

To solve for \( x \):

1. **Divide both sides by 7** to isolate \( x \):

  \[

  x = \frac{1}{7}

  \]

2. **Conclusion:**

  Therefore, \( 7x = 1 \) implies \( x = \frac{1}{7} \).

### 2. \( \frac{2}{9}x = 2 \)

To solve for \( x \):

1. **Multiply both sides by 9** to eliminate the fraction:

  \[

  2x = 2 \cdot 9 = 18

  \]

2. **Divide both sides by 2** to solve for \( x \):

  \[

  x = \frac{18}{2} = 9

  \]

3. **Conclusion:**

  Therefore, \( \frac{2}{9}x = 2 \) implies \( x = 9 \).

### 3. \( \frac{4}{7}x = 1 \)

To solve for \( x \):

1. **Multiply both sides by 7** to eliminate the fraction:

  \[

  4x = 7 \cdot 1 = 7

  \]

2. **Divide both sides by 4** to solve for \( x \):

  \[

  x = \frac{7}{4}

  \]

3. **Conclusion:**

  Therefore, \( \frac{4}{7}x = 1 \) implies \( x = \frac{7}{4} \).

### 4. \( \frac{17}{19}x = 1 \)

To solve for \( x \):

1. **Multiply both sides by 19** to eliminate the fraction:

  \[

  17x = 19 \cdot 1 = 19

  \]

2. **Divide both sides by 17** to solve for \( x \):

  \[

  x = \frac{19}{17}

  \]

3. **Conclusion:**

  Therefore, \( \frac{17}{19}x = 1 \) implies \( x = \frac{19}{17} \).

### Summary of Solutions:

1. \( 7x = 1 \) ⟶ \( x = \frac{1}{7} \)

2. \( \frac{2}{9}x = 2 \) ⟶ \( x = 9 \)

3. \( \frac{4}{7}x = 1 \) ⟶ \( x = \frac{7}{4} \)

4. \( \frac{17}{19}x = 1 \) ⟶ \( x = \frac{19}{17} \)

These steps outline how each equation is solved to find the value of \( x \).

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.