Which step has an incorrect instruction?
| 2 | Simplify by combining like terms. | $-\frac{5}{2}+x=-\frac{7}{4}$ |
|---|---|---|
| 3 | Use the addition property of equality. | $-\frac{5}{2}+\frac{5}{2}+x=-\frac{7}{4}+\frac{5}{2}$ |
| 4 | Use multiplication to find equivalent fractions. | $-\frac{5}{2}+\frac{5}{2}+x--\frac{7}{4}+\frac{10}{4}$ |
| | Simplify by combining like terms. | $x=\frac{3}{4}$ |
Step 1
Step 2
Step 3
Step 4
Answer (2)
Step 2 incorrectly instructs to simplify by combining like terms when it's just restating the equation.
Step 3 correctly uses the addition property of equality.
Step 4 correctly finds equivalent fractions.
Therefore, Step 2 has the incorrect instruction. St e p 2
Explanation
Problem Analysis The problem presents a series of algebraic steps to solve for x in the equation − 2 5 + x = − 4 7 . The goal is to identify the step with the incorrect instruction.
Analyzing Step 2 Step 2 states: Simplify by combining like terms. The equation is − 2 5 + x = − 4 7 . There are no like terms to combine on the left side at this point. This step is simply restating the original equation.
Analyzing Step 3 Step 3 states: Use the addition property of equality. Add 2 5 to both sides: − 2 5 + 2 5 + x = − 4 7 + 2 5 . This step correctly applies the addition property of equality.
Analyzing Step 4 Step 4 states: Use multiplication to find equivalent fractions. Rewrite the right side with a common denominator: − 2 5 + 2 5 + x = − 4 7 + 4 10 . This step correctly finds equivalent fractions to combine the terms on the right side.
Conclusion The incorrect instruction is in Step 2, as it is not a simplification step but rather the initial equation. The simplification occurs later.
Examples
Understanding how to solve linear equations is crucial in many real-world scenarios. For instance, imagine you're trying to figure out how many hours you need to work to save up for a new bicycle. If the bicycle costs $200 and you earn $10 per hour, you can set up the equation 10 x = 200 , where x is the number of hours you need to work. Solving this equation helps you determine that you need to work 20 hours. Similarly, understanding algebraic manipulations is essential for budgeting, calculating discounts, and various other financial and everyday calculations.
The incorrect instruction is in Step 2, which suggests simplifying the original equation by combining like terms, but there are no like terms to combine. Steps 3 and 4 correctly follow the process of solving the equation. Therefore, Step 2 is the one that contains the error.
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