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Question #1 *
If
RS=59 and
ST=10 x-31, find
x
Your answer

Question # $1$ * $\newline$ If $\newline$ $RS=59$ and $\newline$ $ST=10x-31$ , find $\newline$ $x$ $\newline$ Your answer

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Composition of linear functions: find a value

Full solution

Q. Question #

1

*

\newline

If

\newline

RS=59

and

\newline

ST=10x-31

, find

\newline

x

\newline

Your answer

Understand Relationship: Understand the relationship between $RS$ and $ST$ . Since $RS$ and $ST$ are segments of a line or parts of a geometric figure, and they are given in terms of $x$ , we can assume that $RS + ST$ represents the total length of a line or the sum of both segments. We need to set up an equation that relates $RS$ and $ST$ .
Set Up Equation: Set up the equation. $\newline$ We know that $RS = 59$ and $ST = 10x - 31$ . If $RS$ and $ST$ are consecutive segments, then their sum should be equal to the total length. Therefore, we can write the equation as: $\newline$ $RS + ST = 59 + (10x - 31)$
Simplify Equation: Simplify the equation. $\newline$ Now we simplify the right side of the equation: $\newline$ $59 + (10x - 31) = 59 + 10x - 31$ $\newline$ $59 + 10x - 31 = 10x + 28$
Equating RS and ST: Since $RS + ST$ represents the total length, and $RS$ is given as $59$ , we can equate $RS$ to the simplified expression of $ST$ . $\newline$ $59 = 10x + 28$
Solve for x: Solve for x. $\newline$ Now we will isolate $x$ by subtracting $28$ from both sides of the equation: $\newline$ $59 - 28 = 10x + 28 - 28$ $\newline$ $31 = 10x$
Divide for x Value: Divide both sides by $10$ to find the value of $x$ . $\frac{31}{10} = \frac{10x}{10}$ $3.1 = x$

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