Question

Solve for c.

Solve for x.

Solve for c.

Solve for x.

Solve for x.

Answer 1

1) c = 9 - a + b

2) x=-2 or x=3

3) c = 9 - a + b

4) X= 11/3

5) x=-2 or x=3

Answer 2

1) The option
`c=9-a+b` is correct.

2) The option x=-2 or x=-3 is correct.

3) The option
`c=9-a+b` is correct.

4) The option
`x=(11)/(3)` is correct.

5) The option x=-2 or x=-3 is correct.

Explanation:

1) Given equation is
`√(a-b+c)=3`

Now to solve the equation for c:

`√(a-b+c)=3`

Squaring on both sides we get

`(√(a-b+c))^2=3^2`

`a-b+c=9`

`c=9-a+b`

Therefore the option
`c=9-a+b` is correct.

2) Given equation is
`√(3x+10)=x+4`

Now to solve the equation for x:

`√(3x+10)=x+4`

Squaring on both sides we get

`(√(3x+10))^2=(x+4)^2`

`3x+10=x^2+8x+16`

`x^2+8x+16-3x-10=0`

`x^2+5x+6=0` which is a quadratic equation in x.

We can solve it by finding factors

`x^2+5x+6=(x+2)(x+3)`

`(x+2)(x+3)=0`

x+2=0 or x+3=0

Therefore x=-2 or x=-3

Therefore the option x=-2 or x=-3 is correct.

3) Given equation is
`√(a-b+c)=3`

Now to solve the equation for c:

`√(a-b+c)=3`

Squaring on both sides we get

`(√(a-b+c))^2=3^2`

`a-b+c=9`

`c=9-a+b`

Therefore the option
`c=9-a+b` is correct.

4) Given equation is
`√(x+3)=2√(x-2)`

Now to solve the equation for x:

`√(x+3)=2√(x-2)`

Squaring on both sides we get

`(√(x+3))^2=(2√(x-2))^2`

`x+3=2^2(x-2)`

`x+3=4(x-2)`

`x+3=4x-8`

`4x-8-x-3=0`

`3x-11=0`

`x=(11)/(3)`

Therefore the option
`x=(11)/(3)` is correct.

5) Given equation is
`√(3x+10)=x+4`

Now to solve the equation for x:

`√(3x+10)=x+4`

Squaring on both sides we get

`(√(3x+10))^2=(x+4)^2`

`3x+10=x^2+8x+16`

`x^2+8x+16-3x-10=0`

`x^2+5x+6=0` which is a quadratic equation in x.

We can solve it by finding factors

`x^2+5x+6=(x+2)(x+3)`

`(x+2)(x+3)=0`

x+2=0 or x+3=0

Therefore x=-2 or x=-3

Therefore the option x=-2 or x=-3 is correct.