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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 \( x \).