Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 05, 2023

Find $U V$ given $U V=x+2, V W=4$ , and $U W=2 x-3$ . Simplify the answer as a fraction or integer.

STEP 1

Assumptions1. $UV = x +$ . $VW =4$
3. $W =x -3$
4. $W = UV + VW$

STEP 2

We can express $W$ in terms of $UV$ and $VW$ .
$W = UV + VW$

STEP 3

Now, plug in the given values for $UV$ , $VW$ , and $W$ into the equation.
$2x -3 = x +2 +$

STEP 4

implify the right-hand side of the equation.
$2x -3 = x +6$

STEP 5

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$2x - x = +3$

STEP 6

implify both sides of the equation.
$x =9$

STEP 7

Now that we have the value of $x$ , we can substitute it into the equation for $UV$ to find the value of $UV$ .
$UV = x +2$

STEP 8

Plug in the value for $x$ into the equation.
$UV = +2$

STEP 9

Calculate the value of $UV$ .
$UV =9 +2 =11$ So, $UV =11$ .

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