Answer :
To determine which equation is equivalent to the given equation [tex]\(1.43p + 2.2 = -4.001\)[/tex], we can eliminate the decimals by multiplying every term by 100. This process involves transforming each coefficient and constant to maintain the equation's balance while making all the numbers whole numbers.
1. Original Equation:
[tex]\[1.43p + 2.2 = -4.001\][/tex]
2. Multiply Each Term by 100:
This helps remove the decimals:
[tex]\[(1.43 \times 100)p + (2.2 \times 100) = -4.001 \times 100\][/tex]
3. Calculate Terms:
[tex]\[143p + 220 = -400.1\][/tex]
Here, [tex]\(-400.1\)[/tex] still has a decimal. To make every number an integer, we'll multiply the entire equation by 10.
4. Multiply Each Term by 10 to Clear the Decimal:
[tex]\[(143 \times 10)p + (220 \times 10) = -400.1 \times 10\][/tex]
5. Calculate the New Equation:
[tex]\[1430p + 2200 = -4001\][/tex]
This final equation [tex]\(1430p + 2200 = -4001\)[/tex] is equivalent to the original equation, but with whole numbers. Therefore, the correct choice from the given options is:
[tex]\(1430p + 2200 = -4001\)[/tex]
1. Original Equation:
[tex]\[1.43p + 2.2 = -4.001\][/tex]
2. Multiply Each Term by 100:
This helps remove the decimals:
[tex]\[(1.43 \times 100)p + (2.2 \times 100) = -4.001 \times 100\][/tex]
3. Calculate Terms:
[tex]\[143p + 220 = -400.1\][/tex]
Here, [tex]\(-400.1\)[/tex] still has a decimal. To make every number an integer, we'll multiply the entire equation by 10.
4. Multiply Each Term by 10 to Clear the Decimal:
[tex]\[(143 \times 10)p + (220 \times 10) = -400.1 \times 10\][/tex]
5. Calculate the New Equation:
[tex]\[1430p + 2200 = -4001\][/tex]
This final equation [tex]\(1430p + 2200 = -4001\)[/tex] is equivalent to the original equation, but with whole numbers. Therefore, the correct choice from the given options is:
[tex]\(1430p + 2200 = -4001\)[/tex]
