Question

Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52

Answer 1

`\large\boxed{\textsf{See Below.}}`

Explanation:

`\textsf{We are asked to solve for the values of x, given values to select from.}`

`\textsf{Instead of using the FOIL Method, we can simply substitute in the given options}`

`\textsf{then identify if the two expressions are actually equal to each other. This is}`

`\textsf{the \underline{Substitution Property of Equality}.}`

`\large\underline{\textsf{What is the Substitution Property of Equality?}}`

`\textsf{The Substitution Property of Equality is a property that allows us to substitute in}`

`\textsf{a known value for a placeholder, or an unknown variables and the equation will}`

`\textsf{still remain equal. However for our problem we are given the value of x, but we're}`

`\textsf{not certain that the value will make the equation true. That's why we should}`

`\textsf{check every option provided.}`

`\large\underline{\textsf{Use the Substitution Property of Equality;}}`

`\textsf{Our first option given is -46. Substitute that value in for x.}`

`\tt (-46 - 3)^(2) = 49`

`\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}`

`\tt (-46 -3)^(2)=(-49)^(2)=(-49 * -49)=2401.`

`\tt 2401 \\eq 49.`

`\textsf{-46 is not a value of x.}`

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`\textsf{Our second option given is -4. Substitute that value in for x.}`

`\tt (-4 - 3)^(2) = 49`

`\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}`

`\tt (-4 -3)^(2)=(-7)^(2)=(-7 * -7)=49.`

`\tt 49 = 49. \large\checkmark`

`\large\boxed{\textsf{-46 is a value of x.}}`

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`\textsf{Our third option given is 10. Substitute that value in for x.}`

`\tt (10 - 3)^(2) = 49`

`\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}`

`\tt (10 -3)^(2)=(7)^(2)=(7 * 7)=49.`

`\tt 49 = 49. \large\checkmark`

`\large\boxed{\textsf{10 is a value of x.}}`

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`\textsf{Our last option given is 52. Substitute that value in for x.}`

`\tt (52 - 3)^(2) = 49`

`\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}`

`\tt (52 -3)^(2)=(49)^(2)=(49 * 49)=2401.`

`\tt 2401 \\eq 49.`

`\textsf{52 is not a value of x.}`