Question
Solve the proportion. \[ \begin{array}{l}\frac{2}{7}=\frac{6}{x+4} \\ x=\square(\text { Type an integer or a simplified fraction.) }\end{array} \]
Ask by Davies Higgins. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x=17 \)
Solution
We start with the proportion:
\[
\frac{2}{7}=\frac{6}{x+4}.
\]
To solve for \( x \), we cross-multiply:
\[
2(x+4)=7\cdot6.
\]
Simplify both sides:
\[
2x+8=42.
\]
Subtract \( 8 \) from both sides:
\[
2x=34.
\]
Divide both sides by \( 2 \):
\[
x=17.
\]
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Simplify this solution Mind Expander
To solve the proportion \(\frac{2}{7} = \frac{6}{x + 4}\), we can use cross-multiplication. This means we multiply the numerator of one fraction by the denominator of the other fraction: \[ 2(x + 4) = 6 \times 7 \] Now let's perform the multiplication: \[ 2(x + 4) = 42 \] Next, we distribute the 2 on the left side: \[ 2x + 8 = 42 \] Now, to isolate \(x\), we subtract 8 from both sides: \[ 2x = 42 - 8 \] \[ 2x = 34 \] Now, divide both sides by 2: \[ x = \frac{34}{2} \] \[ x = 17 \] Thus, the solution is: \[ x = 17 \]
