Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.) A. 5x+3 =11 B.12x+6 =-4 C.100x =50(x+3) D. 6(x+4) =x+24

Verified step by step guidance

1. Step 1: Solve equation A: $5x+3=11$. Subtract 3 from both sides to isolate the term with $x$.
2. Step 2: Solve equation B: $12x+6=-4$. Subtract 6 from both sides to isolate the term with $x$.
3. Step 3: Solve equation C: $100x=50(x+3)$. Distribute the 50 on the right side and then simplify.
4. Step 4: Solve equation D: $6(x+4)=x+24$. Distribute the 6 on the left side and then simplify.
5. Step 5: Analyze the solutions of each equation to determine which one cannot represent the number of pennies, considering that the number of pennies must be a non-negative integer.

Key Concepts

Linear Equations

Linear equations are mathematical statements that express the equality of two linear expressions. They typically take the form ax + b = c, where a, b, and c are constants, and x is the variable. Understanding how to manipulate and solve these equations is essential for determining the value of x in various contexts.

Solution of an Equation

The solution of an equation is the value of the variable that makes the equation true. For example, in the equation 5x + 3 = 11, solving for x involves isolating the variable to find its value. An equation may have one solution, no solution, or infinitely many solutions, which is crucial for evaluating the validity of the equations presented.

Identifying Extraneous Solutions

Extraneous solutions are values that emerge from the algebraic manipulation of an equation but do not satisfy the original equation. When solving equations, especially those involving variables on both sides or products, it is important to check if the solutions are valid within the context of the problem, as some may not represent feasible scenarios.