Question

solve the literal equation for y.

1. y + 5x = 17
2. 4y - 36x = 28
3. 8x - 11 = 13 + 8y
4. 6 + \frac{1}{3}y = 10 + 12x

solve the literal equation for x.

1. y = 9x - 2x
2. d = 5x + 10xf
3. rx - sx = p
4. 3j = 4kx + 7mx + n

solve the equation for the indicated variable.

1. volume of a cylinder: v = \frac{1}{3}\pi r^{2}h; solve for h.
2. perimeter of a rectangle: p = 2\ell + 2w; solve for w.
3. area of a rectangle: a = \ell w; solve for \ell.
4. the surface area of a right - circular cylinder is given by the formula s = 2\pi rh+2\pi r^{2}. solve the equation for h.

Explanation:

Step1: Isolate y in \(y + 5x=17\)

Subtract \(5x\) from both sides: \(y=17 - 5x\)

Step2: Isolate y in \(4y-36x = 28\)

First, add \(36x\) to both sides: \(4y=28 + 36x\). Then divide both sides by 4: \(y = 7+9x\)

Step3: Isolate y in \(8x - 11=13 + 8y\)

First, subtract 13 from both sides: \(8x-24 = 8y\). Then divide both sides by 8: \(y=x - 3\)

Step4: Isolate y in \(6+\frac{1}{3}y=10 + 12x\)

First, subtract 6 from both sides: \(\frac{1}{3}y=4 + 12x\). Then multiply both sides by 3: \(y = 12+36x\)

Step5: Isolate x in \(y = 9x-2x\)

Combine like - terms: \(y = 7x\), then divide both sides by 7: \(x=\frac{y}{7}\)

Step6: Isolate x in \(d = 5x+10xf\)

Factor out x: \(d=x(5 + 10f)\). Then divide both sides by \(5 + 10f\) (\(f
eq-\frac{1}{2}\)): \(x=\frac{d}{5(1 + 2f)}\)

Step7: Isolate x in \(rx-sx=p\)

Factor out x: \(x(r - s)=p\). Then divide both sides by \(r - s\) (\(r
eq s\)): \(x=\frac{p}{r - s}\)

Step8: Isolate x in \(3j=4kx+7mx + n\)

First, combine the x - terms: \(3j=(4k + 7m)x + n\). Then subtract n from both sides: \(3j - n=(4k + 7m)x\). Finally, divide both sides by \(4k + 7m\) (\(4k+7m
eq0\)): \(x=\frac{3j - n}{4k + 7m}\)

Step9: Isolate h in \(V=\frac{1}{3}\pi r^{2}h\)

Multiply both sides by 3 to get \(3V=\pi r^{2}h\). Then divide both sides by \(\pi r^{2}\): \(h=\frac{3V}{\pi r^{2}}\)

Step10: Isolate w in \(P = 2l+2w\)

First, subtract \(2l\) from both sides: \(P - 2l=2w\). Then divide both sides by 2: \(w=\frac{P - 2l}{2}\)

Step11: Isolate l in \(A=lw\)

Divide both sides by w (\(w
eq0\)): \(l=\frac{A}{w}\)

Step12: Isolate h in \(S = 2\pi rh+2\pi r^{2}\)

First, subtract \(2\pi r^{2}\) from both sides: \(S - 2\pi r^{2}=2\pi rh\). Then divide both sides by \(2\pi r\) (\(r
eq0\)): \(h=\frac{S - 2\pi r^{2}}{2\pi r}\)

Answer:

1. \(y=17 - 5x\)
2. \(y = 7+9x\)
3. \(y=x - 3\)
4. \(y = 12+36x\)
5. \(x=\frac{y}{7}\)
6. \(x=\frac{d}{5(1 + 2f)}\)
7. \(x=\frac{p}{r - s}\)
8. \(x=\frac{3j - n}{4k + 7m}\)
9. \(h=\frac{3V}{\pi r^{2}}\)
10. \(w=\frac{P - 2l}{2}\)
11. \(l=\frac{A}{w}\)
12. \(h=\frac{S - 2\pi r^{2}}{2\pi r}\)