I need help with these questions

1) https://vle.mathswatch.co.uk/images/questions/question2305.png

2) https://vle.mathswatch.co.uk/images/questions/question2318.png

3) https://vle.mathswatch.co.uk/images/questions/question2327.png

Guest Sep 24, 2018

#1**+1 **

Here is the first one:

Solve for g:

w = 7 - sqrt(g)

Reverse the equality in w = 7 - sqrt(g) in order to isolate g to the left hand side.

w = 7 - sqrt(g) is equivalent to 7 - sqrt(g) = w:

7 - sqrt(g) = w

Isolate terms with g to the left hand side.

Subtract 7 from both sides:

-sqrt(g) = w - 7

Multiply both sides by a constant to simplify the equation.

Multiply both sides by -1:

sqrt(g) = 7 - w

Eliminate the square root on the left-hand side.

Raise both sides to the power of two:

** g = (7 - w)^2 = w^2 - 14 w + 49**

Guest Sep 24, 2018

#2**+1 **

Here is the second one:

Solve for w:

y - aw = 2w - 1

Isolate w to the left-hand side.

Subtract 2 w + y from both sides:

w (-a - 2) = -y - 1

Solve for w.

Divide both sides by -a - 2:

** w = (y + 1) / (a + 2)**

Guest Sep 24, 2018

#3**+1 **

Here is the third one:

Solve for t:

q = (2 - 4 t)/(t + 3)

Reverse the equality in q = (2 - 4 t)/(t + 3) in order to isolate t to the left hand side.

q = (2 - 4 t)/(t + 3) is equivalent to (2 - 4 t)/(t + 3) = q:

(2 - 4 t)/(t + 3) = q

Multiply both sides by a polynomial with respect to t to clear fractions.

Multiply both sides by t + 3:

2 - 4 t = q (t + 3)

Write the linear polynomial on the right-hand side in standard form.

Expand out terms of the right hand side:

2 - 4 t = 3 q + qt

Isolate t to the left-hand side.

Subtract q t + 2 from both sides:

t (-q - 4) = 3 q - 2

Solve for t.

Divide both sides by -q - 4:

**t = (2 - 3q) /( q + 4)**

Guest Sep 24, 2018