Answer :
To rewrite the equation 2.3p - 10.1 = 6.5p - 4 - 0.01p using properties, distribute the 6.5p and combine like terms to simplify. Options b and c have the same solution as the original equation.
To rewrite the equation 2.3p - 10.1 = 6.5p - 4 - 0.01p using properties, we can use the distributive property and combine like terms to simplify. Here are the steps: Distribute the 6.5p to both terms on the right side: 6.5p - 0.01p = 6.49p. Combine like terms on the right side: -4 + 6.49p = 6.49p - 4. The rewritten equation is 2.3p - 10.1 = 6.49p - 4.. By combining like terms in the original equation, you end up with the equivalent equation of 2.3p – 10.1 = 6.49p – 4. Hence, Option 'b' is correct. d equivalent equations to 2.3p – 10.1 = 6.5p – 4 – 0.01p. This can be simplified using the properties of equality. The solutions that are equivalent to the given equation are ones that when simplified will give that exact form. Combine like terms on the right side: 6.5p - 0.01p = 6.49p. So your equation 2.3p – 10.1 = 6.49p – 4 is the correct equation which corresponds with option b. But for option 'a', combining 6.5p and -0.01p doesn't give you 6.4p, so the solutions will be different. Option 'c' involves a mistake in moving the decimal place in the 4 on the right-hand side, so solutions will also be different. Option 'd' is also incorrect as 4 is not the same as 40. The final option 'e' changes the coefficient on the left side so it isn't equivalent either.
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Final answer:
To rewrite the given equation and find the equations that have the same solution, simplify both sides using the distributive property and combine like terms to isolate p. The equations with the same solution are 2.3p – 10.1 = 6.4p – 4 and 2.3p – 10.1 = 6.49p – 4.
Explanation:
To rewrite the given equation and find the equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p, we can begin by simplifying both sides of the equation using the distributive property. This will allow us to combine like terms on each side, so we can isolate the variable p.
Step 1: Distribute on the right side of the equation:
2.3p – 10.1 = 6.5p – 4 – 0.01p
2.3p – 10.1 = 6.5p – 4 – 0.01p
2.3p – 10.1 = 6.49p – 4
Thus, the equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are:
- 2.3p – 10.1 = 6.4p – 4
- 2.3p – 10.1 = 6.49p – 4
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