Which step has an incorrect instruction?
| | | |
| :-- | :----------------------------------------- | :------------------------------------ |
| 2 | Simplify by combining like terms. | [tex]$\frac{5}{2}+x=\frac{7}{4}$[/tex] |
| 3 | Use the addition property of equality. | [tex]$\frac{5}{2}+\frac{5}{2}+x=\frac{7}{4}+\frac{5}{2}$[/tex] |
| 4 | Use multiplication to find equivalent fractions. | [tex]$\frac{5}{2}+x=\frac{7}{4}+\frac{10}{4}$[/tex] |
| 5 | Simplify by combining like terms. | [tex]$x=\frac{3}{4}$[/tex] |
A. Step 1
B. Step 2
C. Step 3
D. Step 4
Answer (2)
Analyze the given steps to solve the equation 2 5 + x = 4 7 .
Identify that Step 3 incorrectly uses the addition property of equality instead of subtraction.
Note that to isolate x , you must subtract 2 5 from both sides of the equation.
Conclude that Step 3 has the incorrect instruction. St e p 3
Explanation
Analyzing the Problem We are given an equation 2 5 + x = 4 7 and a series of steps attempting to solve for x . Our goal is to identify the step with the incorrect instruction. Let's analyze each step carefully.
Evaluating Step 2 Step 2 states: 'Simplify by combining like terms.' The equation is 2 5 + x = 4 7 . On the left-hand side, 2 5 and x are not like terms, so they cannot be combined. However, the instruction itself isn't incorrect; it's just that there are no like terms to combine at this stage. So, Step 2 is not where the error lies.
Identifying the Error in Step 3 Step 3 states: 'Use the addition property of equality.' The instruction suggests adding 2 5 to both sides, resulting in 2 5 + 2 5 + x = 4 7 + 2 5 . However, to isolate x , we need to subtract 2 5 from both sides of the original equation. The correct operation should be subtracting 2 5 from both sides: x = 4 7 − 2 5 . Therefore, Step 3 contains an incorrect instruction.
Evaluating Step 4 Step 4 states: 'Use multiplication to find equivalent fractions.' This step aims to find a common denominator to combine the fractions on the right side of the equation (which should be a subtraction, as identified in Step 3). The equivalent fractions are correctly found: 4 7 + 4 10 (although it should be 4 7 − 4 10 ).
Evaluating Step 5 Step 5 states: 'Simplify by combining like terms.' This step performs the subtraction (or addition, based on the incorrect Step 3) and arrives at the solution x = 4 3 . However, since Step 3 was incorrect, this result is also incorrect. The correct calculation should be x = 4 7 − 4 10 = − 4 3 .
Conclusion The incorrect instruction is in Step 3. To isolate x , we need to subtract 2 5 from both sides, not add it. Therefore, the answer is Step 3.
Examples
When solving for an unknown variable in an equation, it's like trying to isolate a specific ingredient in a recipe. Each step you take must be the correct operation to 'remove' the other ingredients from the variable's side of the equation. For example, if you have x + 3 = 5 , you subtract 3 from both sides to find x = 2 . This principle is used in many real-world scenarios, such as calculating budgets, determining the amount of materials needed for a project, or even adjusting cooking recipes.
The incorrect instruction is found in Step 3, where instead of adding 2 5 to both sides of the equation, we should have subtracted it to isolate x . Therefore, Step 3 contains the error, making it the incorrect instruction in the sequence provided. The answer is C. Step 3 .
;
