Question

Solve Task 3 Entirely.​

Answer 1

`\textsf{1.} \quad x=5`

`\textsf{2.} \quad\overline{xy}=6`

`\textsf{3.} \quad \overline{yz}=18`

4. Yes

Explanation:

Given:

• 
  `\overline{xz}=24\; \sf inches`

From inspection of the given diagram:

• 
  `\overline{xy}=x+1`

• 
  `\overline{yz}=4x-2`

Question 1

`\textsf{As $\overline{xy}+\overline{yz}=\overline{xz}$ then}:`

`\implies (x+1)+(4x-2)=24`

`\implies x+1+4x-2=24`

`\implies x+4x+1-2=24`

`\implies 5x-1=24`

`\implies 5x-1+1=24+1`

`\implies 5x=25`

`\implies 5x / 5=25 / 5`

`\implies x=5`

Question 2

`\textsf{Substitute the found value of $x=5$ into the expression for $\overline{xy}$}:`

`\implies \overline{xy}=x+1`

`\implies \overline{xy}=5+1`

`\implies \overline{xy}=6`

Question 3

`\textsf{Substitute the found value of $x=5$ into the expression for $\overline{yz}$}:`

`\implies \overline{yz}=4x-2`

`\implies \overline{yz}=4(5)-2`

`\implies \overline{yz}=20-2`

`\implies \overline{yz}=18`

Question 4

`\textsf{Check $\overline{xy}+\overline{yz}=24$ by substituting the found values}:`

`\implies \overline{xy}+\overline{yz}=24`

`\implies 6+18=24`

`\implies 24=24`

`\textsf{Therefore the found values of $\overline{xy}$ and $\overline{yz}$ are correct}.`

Answer 2

1. x = 5

2. xy = 6

3. yz = 18

4. Yes

Explanation:

Hello!

XZ is the sum of Xy and YZ, or the same as 5x - 1.

1.

Given that XZ is 24 and 5x - 1, we can say that they are equal.

Solve for x

• 5x - 1 = 24
• 5x = 25
• x = 5

We solved our first question: x = 5.

2.

We can find XY by substituting 5 for x in x + 1

• x + 1; x = 5
• 5 + 1
• 6

We solved our second question: XY = 6

3.

We can find YZ by substituting 5 for x in 4x - 2

• 4x - 2;x = 5
• 4(5) - 2
• 20 - 2
• 18

We solved our third question: YZ = 18

4.

Yes, 18 + 6 is 24.