Question

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

Answer 1

2.3p - 10.1 = 6.49p - 4

230p - 1010 = 650p - 400 - p

Explanation:

Option 1

Given equation:

`2.3p - 10.1 = 6.5p - 4 - 0.01p`

Collect like terms:

`\implies 2.3p - 10.1 = 6.5p - 0.01p - 4`

Combine like terms:

`\implies 2.3p - 10.1 = (6.5 - 0.01)p - 4`

`\implies 2.3p - 10.1 = 6.49p - 4`

Option 2

Given equation:

`2.3p - 10.1 = 6.5p - 4 - 0.01p`

Multiply each term by 100 by moving the decimal point 2 places to the right:

`\implies 100 \cdot 2.3p - 100 \cdot 10.1 = 100 \cdot 6.5p - 100 \cdot 4 - 100 \cdot 0.01p`

`\implies 230p - 1010 = 650p - 400 - 1p`

Simplify:

`\implies 230p - 1010 = 650p - 400 - p`