Solving Equations and Literal Equations

9G (3.9) Pure Algebra: Solving Literal Equations and Inequalities

Formulas in Biology?

Multiple Choice

$$ax\ +b=c$$

Solve for x:

[Get x by itself on one side of the equation]

• $$x=\frac{c-b}{a}$$

• $$x=\frac{b-c}{a}$$

• $$x=ac-bc$$

• $$x=c-b-a$$

• $$x=\frac{c}{b}-a$$

Multiple Choice

$$ax\ +b=c$$

Solve for a :

[Get a by itself on one side of the equation]

• $$x=\frac{c-b}{a}$$

• $$a=\frac{b-c}{x}$$

• $$a=xc-bc$$

• $$a=c-b-x$$

• $$a=\frac{c-b}{x}$$

Multiple Choice

$$ax\ +b=c$$

Solve for b :

[Get b by itself on one side of the equation]

• $$x=\frac{c-b}{a}$$

• $$b=\frac{a-c}{x}$$

• $$b=\frac{c-x}{a}$$

• $$b=c-ax$$

• $$b=\frac{c-a}{x}$$

Multiple Choice

$$ax\ +b=c$$

Solve for c :

[Get c by itself on one side of the equation]

• $$c=ax+b$$

• $$c=\frac{a-b}{x}$$

• $$b=\frac{c-x}{a}$$

• $$b=c-ax$$

• $$c=\frac{b-a}{x}$$

Multiple Choice

$$5x\ +b=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=5c+b$$

• $$x=\frac{c-b}{5}$$

• $$x=5b$$

• $$x=\frac{b-c}{5}$$

• $$x=\frac{c-5}{b}$$

Multiple Choice

$$5x\ +b=c$$

Solve for b :

[Get b by itself on one side of the equation]

• $$b=5c+x$$

• $$b=c-5x$$

• $$b=5x$$

• $$b=\frac{x-c}{5}$$

• $$b=\frac{c-5}{x}$$

Multiple Choice

$$5x\ +b=c$$

Solve for 5 :

[Get 5 by itself on one side of the equation]

• $$5=ac+x$$

• $$5=\frac{c-b}{x}$$

• $$x=5$$

• $$5=\frac{x-b}{c}$$

• $$5=\frac{b-c}{x}$$

Multiple Choice

$$\ \frac{ax+b}{c}=d$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\frac{dc-b}{a}$$

• $$x=\frac{dc-a}{b}$$

• $$x=\frac{bc-d}{a}$$

• $$x=\frac{ac-dc}{b}$$

• $$x=cd-ba$$

Multiple Choice

$$\ \frac{ax+b}{c}=d$$

Solve for c :

[Get c by itself on one side of the equation]

• $$c=\frac{ax+b}{d}$$

• $$c=\frac{dx+a}{b}$$

• $$c=\frac{bx+d}{a}$$

• $$c=ax+bd$$

• $$c=\frac{ad+b}{x}$$

Multiple Choice

$$\ \frac{ax+b}{c}=d$$

Solve for b :

[Get b by itself on one side of the equation]

• $$b=cd-ax$$

• $$b=dc+ax$$

• $$b=\frac{cx+d}{a}$$

• $$b=\frac{cb}{ax}$$

• $$b=\frac{ad+c}{x}$$

Multiple Choice

$$4x+3x=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\frac{c}{3}-4$$

• $$x=\frac{c}{7}$$

• $$x=7c$$

• $$x=c-7$$

• $$x=c+7$$

Multiple Choice

$$x\left(a+b\right)=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=ca+cb$$

• $$x=\frac{c}{a+b}$$

• $$x=c\left(a+b\right)$$

• $$x=c-a-b$$

• $$x=c+a+b$$

Multiple Choice

$$k\left(d+t\right)=a$$

Solve for k :

[Get k by itself on one side of the equation]

• $$k=\frac{d}{a+t}$$

• $$k=\frac{a}{d+t}$$

• $$k=a\left(d+t\right)$$

• $$k=a-d-t$$

• $$k=a+d+t$$

Multiple Choice

$$ax+bx=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\frac{c}{a}-b$$

• $$x=\frac{c}{a+b}$$

• $$x=c\left(a+b\right)$$

• $$x=c-a-b$$

• $$x=c+a+b$$

Multiple Choice

$$mx+px=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\frac{m}{c+p}$$

• $$x=\frac{c}{m+p}$$

• $$x=c\left(m+p\right)$$

• $$x=c-m-p$$

• $$x=c+m+p$$

Multiple Choice

$$mx-px=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\frac{m}{c-p}$$

• $$x=\frac{c}{m-p}$$

• $$x=c\left(m-p\right)$$

• $$x=c-m+p$$

• $$x=c-m+p$$

Multiple Choice

$$mx=c+px$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\frac{m}{c-p}$$

• $$x=\frac{c}{m-p}$$

• $$x=c\left(m-p\right)$$

• $$x=c-m+p$$

• $$x=c-m+p$$

Multiple Choice

$$ax+bx=c$$

Solve for b :

[Get b by itself on one side of the equation]

• $$b=\frac{c}{x}-a$$

• $$b=dc+ax$$

• $$b=\frac{cx+d}{a}$$

• $$b=\frac{cb}{ax}$$

• $$b=\frac{ad+c}{x}$$

Multiple Choice

$$ax-bx=c$$

Solve for b :

[Get b by itself on one side of the equation]

• $$b=-\frac{c}{x}+a$$

• $$b=\frac{c}{x}-a$$

• $$b=\frac{c}{x}+a$$

• $$b=-\frac{cx}{ax}$$

• $$b=\frac{-ad-c}{x}$$

Multiple Choice

$$ax+by=c$$

Solve for y :

[Get y by itself on one side of the equation]

• $$y=\frac{c-ax}{b}$$

• $$y=\frac{-c+ax}{b}$$

• $$y=c-\frac{ax}{b}$$

• $$y=cx\ -ab$$

• $$y=cb-ax$$

Multiple Choice

$$ax-by=c$$

Solve for y :

[Get y by itself on one side of the equation]

• $$y=\frac{c-ax}{b}$$

• $$y=\frac{-c+ax}{b}$$

• $$y=c-\frac{ax}{b}$$

• $$y=cx\ -ab$$

• $$y=cb-ax$$

Multiple Choice

$$a\cdot b\cdot x^2=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\sqrt[]{\frac{c}{a\cdot b}}$$

• $$x=\sqrt[]{c\cdot a\cdot b}$$

• $$x=\frac{c}{a\cdot b}$$

• $$x=\sqrt[]{c-a\cdot b}$$

• $$y=c-a\cdot b$$

Multiple Choice

$$a\cdot b\cdot x^2=c$$

Solve for b :

[Get b by itself on one side of the equation]

• $$b=\frac{c}{ax^2}$$

• $$b=\frac{c}{ax^{ }}$$

• $$b=c\cdot a\cdot x^2$$

• $$b=c-ax^2$$

• $$b=\frac{ax^2}{c}$$

Multiple Choice

$$\frac{ax^2}{b}=c$$

Solve for a:

[Get a by itself on one side of the equation]

• $$a=\frac{cb}{x^2}$$

• $$a=cb-x^2$$

• $$x=\frac{cb}{a}$$

• $$x=\sqrt[]{\frac{cb}{a}}$$

• $$a=\frac{c\cdot x^2}{b}$$

Multiple Choice

$$\frac{ax^2}{b}=c$$

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\sqrt[]{\frac{c}{a\cdot b}}$$

• $$x=\sqrt[]{c\cdot a\cdot b}$$

• $$x=\frac{c}{a\cdot b}$$

• $$x=\sqrt[]{c-a\cdot b}$$

• $$y=c-a\cdot b$$

Multiple Choice

$$c\ =\ \sqrt[]{\frac{ax}{b}}$$  

Solve for x :

[Get x by itself on one side of the equation]

• $$x=\frac{c^2\cdot b}{a}$$

• $$x=\frac{c\cdot b}{a}$$

• $$x=\frac{c\cdot a}{b}$$

• $$x=\frac{\sqrt[]{c}\cdot b}{a}$$

• $$x=\left(\frac{c\cdot b}{a}\right)^2$$

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