Question
Which equation matches {6}
2x - 20 = 30
x + x - 9 = 1 + x
x^2 - 10 = 15
3x/5 + 4 = 7
2x - 20 = 30
x + x - 9 = 1 + x
x^2 - 10 = 15
3x/5 + 4 = 7
Answers
GPT-4o mini
To determine which equation matches the solution \(x = 6\), we can substitute \(x = 6\) into each equation and check if the left-hand side equals the right-hand side.
1. \(2x - 20 = 30\)
\[
2(6) - 20 = 12 - 20 = -8 \quad (\text{not equal to } 30)
\]
2. \(x + x - 9 = 1 + x\)
\[
6 + 6 - 9 = 1 + 6 \implies 3 = 7 \quad (\text{not equal})
\]
3. \(x^2 - 10 = 15\)
\[
(6)^2 - 10 = 36 - 10 = 26 \quad (\text{not equal to } 15)
\]
4. \(\frac{3x}{5} + 4 = 7\)
\[
\frac{3(6)}{5} + 4 = \frac{18}{5} + 4 = \frac{18}{5} + \frac{20}{5} = \frac{38}{5} \quad (\text{not equal to } 7)
\]
None of the equations match \(x = 6\).
Let's double-check these calculations in detail to ensure their accuracy:
1. **First equation**:
\[2x - 20 = 30\]
\[2(6) - 20 = 12 - 20 = -8\quad \text{(correct)}\]
2. **Second equation**:
\[x + x - 9 = 1 + x\]
\[6 + 6 - 9 = 1 + 6\]
\[3 = 7\quad \text{(correct)}\]
3. **Third equation**:
\[x^2 - 10 = 15\]
\[36 - 10 = 26\quad \text{(correct)}\]
4. **Fourth equation**:
\[\frac{3x}{5} + 4 = 7\]
\[\frac{3(6)}{5} + 4 = \frac{18}{5} + 4 = \frac{38}{5}\quad \text{(correct)}\]
Looking at all four correctly calculated results, none yield a true equation for \(x = 6\). Therefore, there is no equation from the given options that has \(x = 6\) as its solution.
1. \(2x - 20 = 30\)
\[
2(6) - 20 = 12 - 20 = -8 \quad (\text{not equal to } 30)
\]
2. \(x + x - 9 = 1 + x\)
\[
6 + 6 - 9 = 1 + 6 \implies 3 = 7 \quad (\text{not equal})
\]
3. \(x^2 - 10 = 15\)
\[
(6)^2 - 10 = 36 - 10 = 26 \quad (\text{not equal to } 15)
\]
4. \(\frac{3x}{5} + 4 = 7\)
\[
\frac{3(6)}{5} + 4 = \frac{18}{5} + 4 = \frac{18}{5} + \frac{20}{5} = \frac{38}{5} \quad (\text{not equal to } 7)
\]
None of the equations match \(x = 6\).
Let's double-check these calculations in detail to ensure their accuracy:
1. **First equation**:
\[2x - 20 = 30\]
\[2(6) - 20 = 12 - 20 = -8\quad \text{(correct)}\]
2. **Second equation**:
\[x + x - 9 = 1 + x\]
\[6 + 6 - 9 = 1 + 6\]
\[3 = 7\quad \text{(correct)}\]
3. **Third equation**:
\[x^2 - 10 = 15\]
\[36 - 10 = 26\quad \text{(correct)}\]
4. **Fourth equation**:
\[\frac{3x}{5} + 4 = 7\]
\[\frac{3(6)}{5} + 4 = \frac{18}{5} + 4 = \frac{38}{5}\quad \text{(correct)}\]
Looking at all four correctly calculated results, none yield a true equation for \(x = 6\). Therefore, there is no equation from the given options that has \(x = 6\) as its solution.