Question

PQ= 2x
RQ=3x+1
What is the value of x

Answer 1

a. The value of
`\(x\)` is
`\(4\)`.

b.
`\(PQ = 8\) feet` and
`\(QR = 13\) feet.`

Given that
`\(PQ = 2x\)` and
`\(RQ = 3x + 1\)`, and the total length of the line segment
`\(PQ + QR\)` is
`\(21\)` feet, we can set up an equation based on these relationships.

We know that
`\(PQ + QR = 21\)` feet. And according to the given expressions for
`\(PQ\)` and
`\(RQ\)`,
`\(PQ + QR\)` can be expressed as
`\(2x + (3x + 1)\)`.

So, setting up the equation:

`\[2x + (3x + 1) = 21\]`

Solving for
`\(x\)`:

`\[2x + 3x + 1 = 21\]`

`\[5x + 1 = 21\]`

`\[5x = 20\]`

`\[x = 4\]`

Therefore, the answer is
`\(4\)`.

Now that we have found
`\(x = 4\)`, let's substitute this value back into the expressions for
`\(PQ\)` and
`\(RQ\)` to find their lengths.

`\(PQ = 2x = 2 * 4 = 8\) feet`

`\(RQ = 3x + 1 = 3 * 4 + 1 = 12 + 1 = 13\) feet`

The complete question is here:

Consider the line segment below that is
`$21 \mathrm{ft}$` long.( See the image below)

`$$\begin{aligned}& P Q=2 x \\& R Q=3 x+1\end{aligned}$$`

What is the value of x ?

`$$x=$$`

What is the value of segment PQ and segment QR ?

`PQ=`

`$Q R=$`