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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]
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 \( x \).
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