Questions: Solve for (c). [ frac23=frac7c-4 ] Simplify your answer as much as possible. [ c= ]

$Solve for (c). [ frac23=frac7c-4 ] Simplify your answer as much as possible. [ c= ]$

Transcript text: Solve for $c$. \[ \frac{2}{3}=\frac{7}{c}-4 \] Simplify your answer as much as possible. \[ c= \]

Solution

Solution Steps

To solve the equation $\frac{2}{3} = \frac{7}{c} - 4$, we first isolate the term containing $c$ by adding 4 to both sides. Then, we solve for $c$ by taking the reciprocal of the resulting expression.

Step 1: Isolate the Variable

Starting with the equation: \[ \frac{2}{3} = \frac{7}{c} - 4 \] we add 4 to both sides to isolate the term with $c$: \[ \frac{2}{3} + 4 = \frac{7}{c} \]

Step 2: Combine the Left Side

To combine the left side, we convert 4 into a fraction with a common denominator: \[ 4 = \frac{12}{3} \] Thus, we have: \[ \frac{2}{3} + \frac{12}{3} = \frac{14}{3} \] This gives us: \[ \frac{14}{3} = \frac{7}{c} \]

Step 3: Cross-Multiply and Solve for $c$

Cross-multiplying yields: \[ 14c = 21 \] Now, we solve for $c$ by dividing both sides by 14: \[ c = \frac{21}{14} = \frac{3}{2} = 1.5 \]