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# Questions

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194
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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

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

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)

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)

Sep 24, 2018