Solve the equations to find the number and type of solutions.
The equation $8-4 x=0$ has $\square$ real solution(s).
Answer (1)
Solve the equation 8 − 4 x = 0 for x .
Isolate x by subtracting 8 from both sides and then dividing by -4.
Find the solution x = 2 .
Conclude that the equation has 1 real solution.
Explanation
Understanding the Problem We are given the equation 8 − 4 x = 0 and asked to find the number of real solutions.
Isolating x To solve the equation, we want to isolate x . First, subtract 8 from both sides of the equation: 8 − 4 x − 8 = 0 − 8
− 4 x = − 8
Solving for x Next, divide both sides by -4: − 4 − 4 x = − 4 − 8
x = 2
Determining the Number of Real Solutions The solution x = 2 is a real number. Since we found one solution, the equation has 1 real solution.
Final Answer Therefore, the equation 8 − 4 x = 0 has 1 real solution.
Examples
Imagine you're baking a cake and need to divide your batter evenly. If you have 8 cups of batter and each cake tin requires 4 cups, the equation 8 − 4 x = 0 helps you determine how many cake tins ( x ) you can fill. Solving this simple linear equation ensures you use all the batter without any waste, demonstrating a practical application of basic algebra in everyday tasks.
