Solve [tex]x-\frac{1}{4}=\frac{1}{2}[/tex] for [tex]x[/tex].
A. [tex]x=\frac{1}{4}[/tex]
B. [tex]x=\frac{3}{6}[/tex]
C. [tex]x=\frac{3}{4}[/tex]
D. [tex]x=\frac{5}{8}[/tex]
Answer (2)
Add 4 1 to both sides of the equation: x = 2 1 + 4 1 .
Find a common denominator: x = 4 2 + 4 1 .
Add the fractions: x = 4 3 .
The solution is 4 3 .
Explanation
Understanding the Problem We are given the equation x − 4 1 = 2 1 and asked to solve for x . This is a linear equation in one variable, and we can solve it by isolating x on one side of the equation.
Isolating x To isolate x , we need to add 4 1 to both sides of the equation. This gives us: x − 4 1 + 4 1 = 2 1 + 4 1 x = 2 1 + 4 1
Finding a Common Denominator Now, we need to add the two fractions on the right side of the equation. To do this, we need to find a common denominator. The least common denominator of 2 and 4 is 4. So, we rewrite 2 1 as 4 2 : x = 4 2 + 4 1
Adding the Fractions Now that the fractions have a common denominator, we can add them: x = 4 2 + 1 x = 4 3
Final Answer Therefore, the solution to the equation is x = 4 3 .
Examples
Imagine you are baking a cake and the recipe calls for 2 1 cup of sugar. However, you only have a 4 1 cup measuring cup. To get the correct amount of sugar, you need to figure out how much more sugar to add to your 4 1 cup. This problem is the same as solving the equation x − 4 1 = 2 1 , where x is the total amount of sugar you need. Solving for x tells you that you need 4 3 cup of sugar in total. So, you would fill your 4 1 cup and then add another 2 1 cup to reach the required 4 3 cup.
To solve the equation x − 4 1 = 2 1 , we add 4 1 to both sides to isolate x , which leads us to x = 4 3 . Therefore, the correct answer is option C: 4 3 .
;
