Question

Solve for c. Solve for x. Solve for c. Solve for x. Solve for x.

Answer 1

Answer:

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

Answer:

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 $x=\frac{11}{3}$ is correct.

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

Step-by-step explanation:

1) Given equation is $\sqrt{a-b+c}=3$

Now to solve the equation for c:

$\sqrt{a-b+c}=3$

Squaring on both sides we get

$(\sqrt{a-b+c})^2=3^2$

$a-b+c=9$

$c=9-a+b$

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

2) Given equation is $\sqrt{3x+10}=x+4$

Now to solve the equation for x:

$\sqrt{3x+10}=x+4$

Squaring on both sides we get

$(\sqrt{3x+10})^2=(x+4)^2$

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

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

$x^2+5x+6=0$ 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 $\sqrt{a-b+c}=3$

Now to solve the equation for c:

$\sqrt{a-b+c}=3$

Squaring on both sides we get

$(\sqrt{a-b+c})^2=3^2$

$a-b+c=9$

$c=9-a+b$

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

4) Given equation is $\sqrt{x+3}=2\sqrt{x-2}$

Now to solve the equation for x:

$\sqrt{x+3}=2\sqrt{x-2}$

Squaring on both sides we get

$(\sqrt{x+3})^2=(2\sqrt{x-2})^2$

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

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

$x+3=4x-8$

$4x-8-x-3=0$

$3x-11=0$

$x=\frac{11}{3}$

Therefore the option $x=\frac{11}{3}$ is correct.

5) Given equation is $\sqrt{3x+10}=x+4$

Now to solve the equation for x:

$\sqrt{3x+10}=x+4$

Squaring on both sides we get

$(\sqrt{3x+10})^2=(x+4)^2$

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

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

$x^2+5x+6=0$ 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.