Question

Can you please help me

Answer 1

AB = 3x + 4

BC = 7x + 9

AB + BC = AC

AC = 143

Let us add AB and BC then equate their sum by 143

`AC=AB+BC=3x+4+7x+9=(3x+7x)+(4+9)`

First, step add the like terms

`AC=10x+13`

Equate AC by its length 143

`10x+13=143`

Now we have an equation to solve it

To solve the equation let us move 13 from the left side to the right side by subtracting 13 from both sides

`\begin{gathered} 10x+13-13=143-13 \\ 10x=130 \end{gathered}`

To find x divide both sides by 10 to move 10 from the left side to the right side

`\begin{gathered} (10x)/(10)=(130)/(10) \\ x=13 \end{gathered}`

Now let us find AB and BC

Substitute x by 13 in each expression

AB = 3(13) + 4 = 39 + 4 = 43

BC = 7(13) + 9 = 91 + 9 = 100

The length of AB is 43 units

The length of BC is 100 units