Questions: Solve the equation. Express num 7/5(3x+4)=x

Solve the equation. Express num 7/5(3x+4)=x
Transcript text: Solve the equation. Express num \[ \frac{7}{5}(3 x+4)=x \]
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Solution

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Solution Steps

Step 1: Distribute the Fraction

To clear the parentheses, distribute \(\frac{7}{5}\) across the terms inside the parentheses:

\[ \frac{7}{5}(3x + 4) = \frac{7}{5} \cdot 3x + \frac{7}{5} \cdot 4 \]

This simplifies to:

\[ \frac{21}{5}x + \frac{28}{5} \]

Step 2: Set the Equation

Set the distributed expression equal to \(x\):

\[ \frac{21}{5}x + \frac{28}{5} = x \]

Step 3: Eliminate the Fraction

Multiply every term by 5 to eliminate the fractions:

\[ 5 \left(\frac{21}{5}x + \frac{28}{5}\right) = 5x \]

This simplifies to:

\[ 21x + 28 = 5x \]

Step 4: Isolate the Variable

Subtract \(5x\) from both sides to isolate terms involving \(x\):

\[ 21x - 5x + 28 = 0 \]

This simplifies to:

\[ 16x + 28 = 0 \]

Step 5: Solve for \(x\)

Subtract 28 from both sides:

\[ 16x = -28 \]

Divide both sides by 16 to solve for \(x\):

\[ x = \frac{-28}{16} \]

Simplify the fraction:

\[ x = -\frac{7}{4} \]

Final Answer

\[ \boxed{x = -\frac{7}{4}} \]

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