Questions: Identify the following as an expression or an equation. Then simplify the expression or solve the equation. (3x/5)+(x/7)=1 Select the correct choice below and fill in the answer box to complete your choice. A. It is an equation and the solution set is . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. It is an expression and its simplified form is . (Use integers or fractions for any numbers in the expression.)

Solution Steps

To determine whether the given mathematical statement is an expression or an equation, we need to check if there is an equality sign. Since there is an equality sign, it is an equation. The next step is to solve the equation for \( x \). We will do this by finding a common denominator for the fractions, combining them, and then isolating \( x \).

The given statement is \(\frac{3x}{5} + \frac{x}{7} = 1\). Since there is an equality sign, it is an equation.

To solve the equation, we first find a common denominator for the fractions \(\frac{3x}{5}\) and \(\frac{x}{7}\). The least common denominator of 5 and 7 is 35.

Rewrite the equation with the common denominator: \[ \frac{21x}{35} + \frac{5x}{35} = 1 \] Combine the fractions: \[ \frac{26x}{35} = 1 \]

To isolate \(x\), multiply both sides of the equation by 35: \[ 26x = 35 \] Divide both sides by 26 to solve for \(x\): \[ x = \frac{35}{26} \]

Final Answer