Question

Solve the equation for h and find the restrictions on the variables:
10h + hx = d - 5

Answer 1

`h=(d-5)/(10+x)`

x ≠ -10

Explanation:

Given equation:

`10h+hx=d-5`

To solve for h, factor out h from the left side of the equation:

`\implies h(10+x)=d-5`

Divide both sides by (10 + x):

`\implies (h(10+x))/(10+x)=(d-5)/(10+x)`

`\implies h=(d-5)/(10+x)`

A rational function is undefined when the denominator is equal to zero.

Therefore, x ≠ -10.

Answer 2

• Solution: h = (d - 5)/(10 + x)
• Restriction: x ≠ - 10

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Given equation:

• 10h + hx = d - 5

Solve the equation for h:

• 10h + hx = d - 5 Given
• h(10 + x) = d - 5 Factor out h
• h = (d - 5)/(10 + x) Divide both sides by (10 + x)

The restriction is about the denominator, it can't be zero:

• 10 + x ≠ 0 ⇒ x ≠ - 10