Question

EASY) write and equation for x then solve for x

Answer 1

`\large\boxed{\tt x = 23^(\circ)}`

Explanation:

`\textsf{We are given 2 \underline{Linear Pairs}. We are asked to form an equation, and to solve for x.}`

`\large\underline{\textsf{What are Linear Pairs?}}`

`\textsf{Linear Pairs are 2 Adjacent Angles that form a 180}^(\circ) \ \textsf{angle, or add up to 180}^(\circ).`

`\textsf{For our problem, these 2 angles given to us are Linear Pairs, which equal 180}^(\circ)`

`\textsf{when added together. Let's create an equation to find x.}`

`\large\boxed{\tt 180^(\circ)=93^(\circ) + (3x+18)^(\circ)}`

`\textsf{Now, let's solve for x by using the \underline{Properties of Equality}.}`

`\large\underline{\textsf{What are the Properties of Equality?}}`

`\textsf{The Properties of Equality are Properties that allow us to manipulate equations.}`

`\textsf{There are 9 properties of equality that we can use, each allowing us to simplify}`

`\textsf{one side of an equation. These properties are mainly used to find missing variables.}`

`\textsf{Let's solve for x by using the Properties of Equality.}`

`\large\underline{\textsf{Solving for x;}}`

`\tt 180^(\circ) = 93^(\circ) + 3x^(\circ)+18^(\circ).`

`\textsf{Let's first Combine Like Terms.}`

`\tt 180^(\circ) = \boxed{\tt 93^(\circ)} + 3x^(\circ)+\boxed{\tt 18^(\circ)}`

`\tt 180^(\circ) = 111^(\circ) + 3x^(\circ)`

`\textsf{Now, let's use the Subtraction Property of Equality which states that if 2 same}`

`\textsf{numbers are subtracted from both sides of the equation, then both expressions}`

`\textsf{still equal each other. Let's subtract 111 from both sides of the equation.}`

`\tt 180^(\circ) - 111^(\circ) = 111^(\circ) - 111^(\circ) + 3x^(\circ)`

`\tt 69^(\circ) = 3x^(\circ)`

`\textsf{Let's use the Division Property of Equality, which is similar to subtraction but it's}`

`\textsf{for division. Divide each side of the equation by 3.}`

`\tt (69^(\circ))/(3) = (3x^(\circ))/(3)`

`\large\boxed{\tt x = 23^(\circ)}`